Press with just enough force to let the note ring clearly, and that’s it! Guitar necks come with different heights of fret wire and there are advantages and disadvantages to both tall and short frets. A neck with short frets lets the fretboard wood stop your finger from pressing any harder – but if you rely on that, you may already be pressing too hard. Not pressing too hard on the string allows your fingers to work more efficiently, and that means faster, smoother movement. That is essential for playing the way you want to sound, with good tone, in tune and in time.
Taller frets (or a scalloped fretboard) make string bending fairly easy. There’s plenty of space between the string and the fingerboard to let you get a good grip. Hammer-ons, pull-offs and the like are also easier. Taller frets might lead to intonation issues though from players pushing too hard (with no fingerboard to stop them) and making the note sharper than intended. I’ve read that going to taller frets also can present a bit of a learning curve for many players. You’ll generally get longer wear out of a taller fret and you can have it dressed more often, although a fret made with harder metal (stainless steel instead of nickel) might solve that problem.
A medium-height fret is probably a better choice for most players. The majority of guitars come with medium frets installed and most of us are quite happy to play on them. If properly installed, they can usually be dressed a few times before re-fretting or neck replacement is required. If you’re unsure about fret height, go with medium.
Here’s the crux of the biscuit: press until the string hits the wood just enough to make a clear, buzz- free sound. You only need to form a little bridge between the bridge and the fret wire with the string… and you want that bridge to be straight, with the correct tension. If you press any harder, you are flexing the string downward and you are actually bending the note slightly! (John Lagreca points out that if you are playing a long sustained note and you hear it as a little flat, that extra pressure can push your note into the proper intonation). If your intent is to bend the note, you can get more mileage out of a lateral (sideways-on-the-neck) bend than a downward one for sure.
If you learn to use the proper amount of pressure early in your guitar playing that pressure becomes engrained in your muscle memory. You don’t need the fingerboard wood to stop you from pressing too hard, and you’ll sound great on any neck – short, medium or tall frets notwithstanding.