Nobody ever really taught me "Right" or "Wrong" ways to mute while I played. I just figured it out by myself as I played. I play finger-style, with a pick, slap-style, tapping, or chimes (harmonics) and muting techniques vary with each technique.
Basically, as I move across the neck from 4th string to 1st I will mute with my right-hand fingers, and as I move from 1st string to 4th I will mute with my left-hand fingers. I've been doing it for so long (over 30 years) that I'm not even conscious of exactly how I do it.
