When playing finger style, with index and middle, I tend to mute anything lower than the strings I'm playing on with the thumb of my plucking hand. You can also train yourself to use your ring and pinky finger to mute those lower strings, I tend to just use the thumb.
I do most other muting with my left hand.
If you learn to play with your thumb and index finger, or a pick, you can use palm muting with the plucking hand, which I don't normally use to completely mute anything, but to play muted notes.
If you're talking about ringing notes on lower strings that you aren't playing.. learn floating thumb, or moving anchor.. or use your ring and pinky.