It's a combination of muting with both hands. For example, if playing the D or G strings you can mute the E and A with the heel of your pick hand. While playing the E and A, mute the D and G with your fret hand, with whatever fingers are free. This is a very rough guide. Your best bet, I think, is to take a few lessons with a guitarist- after all, they have to master this technique.
Good advice. Taking lessons from a jazz guitarist improved my bass playing technique more than I ever thought possible.