Note that there are less than 2^6 = 64 different Braille symbols available, because some symbols are too easily confused (consider all the symbols, like a, which consist of only a single dot -- the prefix used to indicate capital letters is the one least likely to be confused with a, but it only makes the other four more likely to be confused). Because of this, the Braille system uses prefix characters to indicate capital letters and numbers (using the first ten letters as the digits). Also, each letter represents a common word when used alone.

The Braille alphabet:

 1     2     3     4     5     6     7     8     9     
 a     b     c     d     e     f     g     h     i     j
* .   * .   * *   * *   * .   * *   * *   * .   . *   . *
. .   * .   . .   . *   . *   * .   * *   * *   * .   * *
. .   . .   . .   . .   . .   . .   . .   . .   . .   . .

 k     l     m     n     o     p     q     r     s     t
* .   * .   * *   * *   * .   * *   * *   * .   . *   . *
. .   * .   . .   . *   . *   * .   * *   * *   * .   * *
* .   * .   * .   * .   * .   * .   * .   * .   * .   * .

 u     v     x     y     z     w     capital     number 
* .   * .   * *   * *   * .   . *      . .        . * 
. .   * .   . .   . *   . *   * *      . .        . * 
* *   * *   * *   * *   * *   . *      . *        * * 

Source: Merriam-Webster's New International Dictionary, Second Edition and Merriam-Webster's Third New International Dictionary.

NI2 says other dot patterns are used for other common words and punctuation and partial words. If anybody has information on this, please add a writeup to this node.