There are several methods but what I do is to tie a string to a thin stick, place the string through the horse's mouth (or pony) with the stick resting lightly against the horse. Mark the other side of the string with a marking pen. I can then measure the distance from the stick to the mark then add about 1/4" or so to get the size bit I need.
If I'm dealing with a standard horse of anywhere from 15 to 16 h, a 5" will normally work. It's when I'm dealing with a pony, a draft, or a large horse that I really need to measure. Most bits will go from go in 1/4' increments below 5" then 1/2' increments from 5 up. Remember that if you measure 5 1/8" (as an example) you will go to a 5 1/2" bit.