So now you're done with the actual brewing of your beer, and you're waiting for those wonderful yeast cells to obligingly turn all of those sugars into alcohol. What can you expect to happen? Well, primary fermentation of an average ale usually takes around two weeks, although a number of factors will affect this. If you're fermenting near the colder end of your yeast's temperature range, the process will be a bit slower. Some variants of yeast also activate and ferment faster than others.
Most of the time, nothing much will happen for the first two to four days, and then suddenly BOOM, your wort will be fermenting like crazy. This initial phase of fermentation is fascinating to watch. Your wort will be a swirling maelstrom, stirred internally by all the gas and energy given off as byproducts of fermentation. The blowoff hose you've attached to the top of your carboy will be expelling all these gases into the layer of water in your bottling bucket. At this point, it is also likely that it will be expelling a fair amount of foam. This foam is made up of bitter resins and other undesirable byproducts which you don't want in your beer anyway. It is probable that these resins and gases will give off unpleasant odors. Don't let this concern you - remember, the fact that this stuff is being given off means it's not going to be in your beer when it's done.
This vigorous fermentation will normally subside after another three to five days. Once this has happened, and the foam level inside the carboy has dropped, you should remove the blowoff hose and replace it with your rubber stopper and fermentation lock. Make sure the fermentation lock is partially filled with water. Again, this will allow gases to escape from the carboy without allowing anything else to come in.
This phase of fermentation will generally last for another week or two. There are a number of ways to tell if fermentation is complete. The scientific way is to use your hydrometer to take daily gravity readings. The hydrometer measures the specific gravity of a liquid. Normal water has a specific gravity of 1. Adding sugars makes a liquid denser and thus increases its specific gravity. Most worts have a specific gravity in the 1.040 - 1.050 range. As fermentation progresses, and these sugars are converted into alcohol, the density will decrease again, and the final gravity of most beers winds up being 1.005 - 1.010 or so. When your hydrometer readings remain stable for several days in a row, this is indicative that fermentation is complete.
While certainly very accurate, this method does have its drawbacks. First, and perhaps most importantly, it is a waste of beer. A hydrometer reading requires only a small amount of beer, but it cannot be returned to the carboy after you take your reading. Two or three weeks of this adds up, and you will wind up with a couple less bottles of beer than you might otherwise. It also takes considerable effort, and these two reasons are why lazy beerhounds like me don't use our hydrometers.
If you don't want to bother with all that hydrometer business, a good way to gauge when your beer is finished fermenting is by watching the bubbles in the fermentation lock. When the bubbling slows down to about once every two minutes or so, this is a good indication that fermentation is pretty much over. At this point, there will be a layer of (mostly dead) yeast cells and other particles on the bottom of your carboy. You are now ready to bottle your first batch of beer. Proceed to the next node, Homebrewing 104: Bottling and Carbonation and we'll walk through it. You may also wish to go back and read Homebrewing 102: The First Batch.
On a final note, it is very important to be patient during the fermentation process. For whatever reason, your beer may just be a little slower. Don't worry about it. The yeast knows what it's doing, and as long as you keep the environment stable, there are very few things that can go wrong here. Relax.