There are two ways to cleanly fret strings. One is to to have your fingers come straight down on the finger board so the fingertips don't touch other strings. The other is to deliberately mute any neighbouring strings you don't want to sound, by letting your fingers or your wrapped around thumb or sometimes the edge of your palm touch them lightly as you pluck the strings you want to sound. Each of these techniques takes practice.

I saw a photo with a closeup of Eric Clapton's left hand one time while he was playing, and he had medium length finger nails, and it occurred to me that he must not play a lot of chords with open strings where you must fret with the tip of your finger. Instead he must play mostly using the pulp of the finger (good for bending notes) and either mutes or avoids striking other strings.