This measurement is taken from the top of the 12th fret, to the bottom of the string, generally with a small metal ruler. As a starting point, the following heights are factory recommendations:
Specifics for Gibson Guitars - measurement is made at the 12th fret.
Height - Bass side Height - Treble side
Specifics for Fender guitars - measurement is made at the 14th fret:
Neck Radius Height - Bass side Height - Treble Side
7.25" 5/64" 4/64"
9.5" to 12" 4/64" 4/64"
15" to 17" 4/64" 3/64"
The height of the string is generally adjusted by turning small allen head screws in the individual string saddles, or by adjusting the treble and bass side of the bridge.A 64th of an inch seems like a small amount, but when you're talking overall string heights of 3/64 to 5/64, a 64th is a significant change! In general, the rule is that as you go from the high to low strings, there should be a gradual increase in height. If you have a fairly radiused fretboard, your strings should follow the radius of the fretboard. If your string height is seriously out of whack, then start by adjusting the thumbwheels on the bridge if you have a Gibson Tune-A-Matic style bridge, to bring it within the ballpark. Then make the fine adjustments using the individual string saddles. If it's pretty close to begin with, you should be able to make all the adjustments by just tweaking the string saddles. Turning the screws clockwise will raise the saddle, counter-clockwise will lower it.
Note: If you have any high frets, or problems with your fretboard, you may not be able to achieve the optimum specifications without first having the problem resolved properly.