When playing with a pick, you gotta do the palm mute thing.
Check out some guitar video's on YouTube...
Basically, you rest your palm on top of / just in front of the bridge saddles...
OOPS! (((adding)))
or wait... You mean like muting strings from ringing, rather than muted tone!
Oh, its all about the left hand muting. I lay my fingers across the top of the strings, and only apply pressure on the string I want to fret, its very slight movements...
This isnt the best video example in the world, but I am only pressing down on the E string with my 1st finger, the other fingers are reaching over muting the B string and the other strings... Your fingers are in a slightly curved shape,
SLaPiNFuNK Bass Vid