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.
I use a thin wooden stick. Mark it red somewhere on the end, put in mouth so that red would be right outside the horse's mouth, and mark another end. Then you have to add 1/4" to the length.