You need to spend a whole bunch of time figuring out what works to mute noises with your fretting hand and basically build up your reportoire over time.
After a couple of years it just comes to you automatically.
Like when I bend a note like this..

G|---7b9---|

...my thumb automatically mutes the 5th and 6th strings and my pinky mutes the 1st and 2nd strings. Or if I'm just playing a single note or scales, the rest of my left hand is usually muting most of the strings in some way in combination with my right hand.
You sorta have to rethink everything from scratch and just learn to think 'clean' all the time.