Folding a signature is the process of folding down a full sheet of paper into several pages, which will make a section of a book - a signature. The most important consideration in folding a signature is that the paper grain must be parallel to the spine of the book, and that the grain in each signature must go in the same direction. (Which it will, if the grain in each signature is parallel to the spine.)

Before folding a sheet of paper, first determine the direction of the grain of the paper – see paper grain. In the two sheets of paper represented below by two rectangles, assume that the direction of the grain is verticalparallel to the side of the screen. The additional lines represent folds.

 _______________
|               |
|               |
|               |
|               |
|               |
|               |
|               |
|               |    ________________________________
|               |   |                                |
|               |   |                                |
|               |   |                                |
|               |   |                                |
|               |   |                                |
|               |   |                                |
|               |   |                                |
|_______________|   |________________________________|

The paper can be folded once to make a folio.
 _______________
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |    ________________________________
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|_______|_______|   |_______________|________________|

Twice to make a quarto.
 _______________
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|_______|_______|    ________________________________
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |_______________|________________|
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|_______|_______|   |_______________|________________|

Three times to make an octavo. (Note that there are four folds visible in the image – these multiple folds occur because the paper has already been folded when that fold is made.)
 _______________
|       |       |
|       |       |
|       |       |
|_______|_______|
|       |       |
|       |       |
|       |       |
|_______|_______|    ________________________________
|       |       |   |       |       |       |        |
|       |       |   |       |       |       |        |
|       |       |   |       |       |       |        |
|_______|_______|   |_______|_______|_______|________|
|       |       |   |       |       |       |        |
|       |       |   |       |       |       |        |
|       |       |   |       |       |       |        |
|_______|_______|   |_______|_______|_______|________|
Or
 _______________
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|___|___|___|___|    ________________________________
|   |   |   |   |   |               |                |
|   |   |   |   |   |_______________|________________|
|   |   |   |   |   |               |                |
|   |   |   |   |   |_______________|________________|
|   |   |   |   |   |               |                |
|   |   |   |   |   |_______________|________________|
|   |   |   |   |   |               |                |
|___|___|___|___|   |_______________|________________|

Or the paper could be folded four times to make a sextodecmio. (These are just a couple of the possible ways to make a sextodecimo. There are others, but they are not really practical to fold.)
 _______________
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|___|___|___|___|
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|___|___|___|___|    ________________________________
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|___|___|___|___|   |___|___|___|___|___|___|___|____|
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|___|___|___|___|   |___|___|___|___|___|___|___|____|
Or
 _______________
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
|_|_|_|_|_|_|_|_|    ________________________________
| | | | | | | | |   |       |       |       |        |
| | | | | | | | |   |_______|_______|_______|________|
| | | | | | | | |   |       |       |       |        |
| | | | | | | | |   |_______|_______|_______|________|
| | | | | | | | |   |       |       |       |        |
| | | | | | | | |   |_______|_______|_______|________|
| | | | | | | | |   |       |       |       |        |
|_|_|_|_|_|_|_|_|   |_______|_______|_______|________|

These are just some of the ways that the paper can be folded to make different size signatures. It is not important that the paper be folded in this specific manner to make a signature with a given number of folds, just that the grain is parallel with the spine.

To actually fold the paper, a bone folder is needed. To make the first fold, gently fold the paper in half (or thirds if you are making a signature of some other size), line up the top corners, and use the bone folder to crease the paper, in a single motion, from the top of the page down. Repeat this until the entire signature is folded. The signatures above will fold down as follows:

Folio:

 _______________
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |    ________________________________
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|_______|_______|   |_______________|________________|

One fold:
 _______
|       |
|       |
|       |
|       |
|       |
|       |
|       |
|       |            _______________
|       |           |               |                
|       |           |               |                
|       |           |               |                
|       |           |               |                
|       |           |               |                
|       |           |               |                
|       |           |               |                
|_______|           |_______________|

Quarto
 _______________
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|       |       |
|_______|_______|    ________________________________
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |_______________|________________|
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|_______|_______|   |_______________|________________|

First fold:
 _______________     ________________________________ 
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |               |                |
|       |       |   |_______________|________________|
|       |       |   
|       |       |    
|       |       |    
|_______|_______|    

Second fold:
 _______             _______________
|       |           |               |                
|       |           |               |                
|       |           |               |                
|       |           |_______________|
|       |          
|       |           
|       |           
|_______|    

Octavo
 _______________
|       |       |
|       |       |
|       |       |
|_______|_______|
|       |       |
|       |       |
|       |       |
|_______|_______|    ________________________________
|       |       |   |       |       |       |        |
|       |       |   |       |       |       |        |
|       |       |   |       |       |       |        |
|_______|_______|   |_______|_______|_______|________|
|       |       |   |       |       |       |        |
|       |       |   |       |       |       |        |
|       |       |   |       |       |       |        |
|_______|_______|   |_______|_______|_______|________|
Or
 _______________
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|___|___|___|___|    ________________________________
|   |   |   |   |   |               |                |
|   |   |   |   |   |_______________|________________|
|   |   |   |   |   |               |                |
|   |   |   |   |   |_______________|________________|
|   |   |   |   |   |               |                |
|   |   |   |   |   |_______________|________________|
|   |   |   |   |   |               |                |
|___|___|___|___|   |_______________|________________|

First fold:
 _______________     
|       |       |  
|       |       |  
|       |       | 
|_______|_______|  
|       |       |   
|       |       |   
|       |       |   
|_______|_______|  
(both become the same shape after the first fold)
Or
 _______________  
|   |   |   |   | 
|   |   |   |   |   
|   |   |   |   |  
|   |   |   |   |    ________________________________
|   |   |   |   |   |               |                |
|   |   |   |   |   |_______________|________________|
|   |   |   |   |   |               |                |
|___|___|___|___|   |_______________|________________|

Second fold:
 _______________     
|       |       |   
|       |       |   
|       |       |   
|_______|_______|  
Or
 _______
|   |   | 
|   |   |    
|   |   |     
|   |   | 
|   |   |    
|   |   |            ________________________________
|   |   |           |               |                |
|___|___|           |_______________|________________|

Third fold:
 _______ 
|       |          
|       |          
|       |          
|_______|  
Or
 ___
|   |    
|   |       
|   |        
|   |    
|   |       
|   |                _______________
|   |               |               |    
|___|               |_______________|

Sextodecimo:
 _______________
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|___|___|___|___|
|   |   |   |   |
|   |   |   |   |
|   |   |   |   |
|___|___|___|___|    ________________________________
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|___|___|___|___|   |___|___|___|___|___|___|___|____|
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|   |   |   |   |   |   |   |   |   |   |   |   |    |
|___|___|___|___|   |___|___|___|___|___|___|___|____|
Or
 _______________
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
| | | | | | | | |
|_|_|_|_|_|_|_|_|    ________________________________
| | | | | | | | |   |       |       |       |        |
| | | | | | | | |   |_______|_______|_______|________|
| | | | | | | | |   |       |       |       |        |
| | | | | | | | |   |_______|_______|_______|________|
| | | | | | | | |   |       |       |       |        |
| | | | | | | | |   |_______|_______|_______|________|
| | | | | | | | |   |       |       |       |        |
|_|_|_|_|_|_|_|_|   |_______|_______|_______|________|

First fold:
 _______________   
|   |   |   |   |   
|   |   |   |   |   
|   |   |   |   |   
|___|___|___|___|   
|   |   |   |   |   
|   |   |   |   |   
|   |   |   |   |   
|___|___|___|___| 
(after the first fold, both are essentially the same)
Or
 _______
| | | | | 
| | | | |  
| | | | |  
| | | | |
| | | | | 
| | | | | 
| | | | | 
|_|_|_|_|                            ________________
| | | | |                           |       |        |
| | | | |                           |_______|________|
| | | | |                           |       |        |
| | | | |                           |_______|________|
| | | | |                           |       |        |
| | | | |                           |_______|________|
| | | | |                           |       |        |
|_|_|_|_|                           |_______|________|

Second fold:
 _______
|   |   | 
|   |   |     
|   |   |   
|___|___| 
|   |   |   
|   |   |    
|   |   |      
|___|___|  
Or
 ___
| | |  
| | |   
| | |   
| | | 
| | |  
| | | 
| | | 
|_|_|                              
| | |                        
| | |                         
| | |                                
| | |                                ________________
| | |                               |       |        |
| | |                               |_______|________|
| | |                               |       |        |
|_|_|                               |_______|________|

Third fold:
 _______
|   |   |   
|   |   |    
|   |   |      
|___|___|  
Or
 ___
| | |                        
| | |                         
| | |                                
| | |                               
| | |                                
| | |                                ________________
| | |                               |       |        |
|_|_|                               |_______|________|

Fourth fold:
 ___
|   |  
|   |     
|   |       
|___|  
Or
 _  
| |                         
| |                          
| |                                 
| |                                
| |                                 
| |                                  _______
| |                                 |       |
|_|                                 |_______|

There are, of course, many other ways that signatures can be folded, many other combinations of folds. These are just the most basic ones. The important thing to remember is that once the folding is completed, the paper grain must be parallel to the spine.