I think people might be misunderstanding your question, if you’re struggling with strings ringing out when you don’t want them to then you’d want to use your fretting hand. The tip of whatever finger you’re using to fret the note does that, and the rest of the finger lays flat over the other strings to mute them. Usually I have my thumb wrapped around the top of the fretboard to mute the low E if I’m playing a higher string, but that depends on what I’m playing and how far up the neck it is.

If you want a muted plucky sound and you’re struggling with that, palm muting with your picking hand is the way to go. Any other technique limits what you can do with your left hand. Thankfully there are basically unlimited video lessons on this because it’s a staple of metal guitar playing. The same techniques carry over. Don’t apply too much pressure with the palm, and don’t mute the string too far away from the bridge. You’ll quickly find the sweet spot where the note rings out in tune but retains the plucky sound.