Strings ring out while playing.

I would consider floating the thumb down to the A string to silence the ringing. You can also use your left hand to mute the A in between notes on the D and G strings.

 

It's hard to explain, but just rock your left ( fretting) hand back (toward you) a little to mute the other strings with the meat of your fingers that you are not using.

 

The best solution would be floating your thumb and using that to mute, or anchoring your thumb on the A whilst playing on the D, on the D whilst playing on the G. If you want to be lazy, you can always mute the A with your pinky or ring finger, but it's poor technique and prevents you from using that finger for anything else.

 

Just rest your thumb on A like you do E. Jack Bruce of Cream does that alot.

 

The best solution is Todd Johnson's version of the floating thumb, it's easier to get the hang of than resting your thumb on E and A strings and more effective.

http://uk.youtube.com/watch?v=PPVMBPmrblU

 

Sounds like sound advice, but I just rest the thumb on the A. Yeah, it may feel a little odd, but just like any technique thing it becomes muscle memory over time. However, since you are not "muscle memorized" and don't have bad habits to break, now is the time to be trying out as many techniques as you can. Easier to learn than unlearn IME.

 

Good advice so far. This all falls under the category of "muting." Basically, you need to touch every string at all times, otherwise it will ring out. You can use different combinations of left and right hand to mute. I personally like to move my right hand thumb so that it is in between the E and A strings, while I am playing on the D or G string. It will feel natural the more you practice it.