Bra sizes are made up of two components
(always measure while wearing your own bra):

An even number that represents the back size (32, 34, 36, etc.) determined by the size of the torso.
(see Figure 1, line A)

A letter that indicates the cup size (A, B, C, etc.) determined by the size of the breast itself.
(see Figure 1, line B)

To determine the back size
(torso measurement):

Using a tape measure, wrap snugly around your ribcage, directly under the breast
(see A in figure above).

Add 5 to the measurement (i.e. if "A is 29", the back size is 34) After 33 inches, only add 3 inches to the back measurement (i.e. if "A is 35", the back size is 38)

Verify the back size:
Measure around the top of your breasts (the line above B in the figure above). This measurement should equal your back size calculation. For example if you measured 29 inches around your ribcage, the calculation is 29 + 5 = 34. The measurement above your breasts should equal 34.

Hints:

If the back size comes out to an uneven number, try the next size up.
If you are in-between sizes or you are having difficulty finding the correct fit, then if you go up in cup size come down in band size or if you go up in band size come down in cup size. For example, if you are wearing a 42D, but it is a little too snug around the band, then you would move up to a 44C.
To determine the cup size (breast measurement):
Have someone stand by your side and bring a tape measure loosely around the fullest part of the bust (see B in figure above). Subtract the back size from this measurement (i.e. if "B" is 37" and the back size ("A" +5) was 34, the difference is 3"). This difference determines the cup size (see chart below).