fret hand muting

i've been getting wierd string noises, and i want to cut down on these noises by using fret hand muting instead of using my picking palm to cut the noises. could someone explain to me how you do this? and any pointers or exercises would help too. also another thing, i get a wierd little twang sound, kinda like a pull off sound, when i have to play to notes that are on the same fret, but different strings. for example:

E--------13-------
B-------------13--

since i have to take my finger off the e string, to fret the b string, i get this annoying little sound when i lift my finger off the E string. would fret hand muting solve this problem? or do i need to do something else with my fretting hand?

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.