Damping is, in my opinion, one of the most difficult parts of playing the guitar. It is a strain on the brain and requires much more concentration and awareness than playing without damping. However, to achieve crisp, clean articulation, damping is essential. There are many damping techniques:
- When playing a note with the thumb, you can angle the thumb slightly towards the next lower string to dampen it.
- When playing with thumb or finger, you can make an elliptical motion back to the string you just played to dampen it.
- You can use any available left-hand finger to dampen a string.
- You can lay the outside of the fourth finger of the right hand across all strings to dampen all of them (for instance at the end of a piece)
- You can do the same with palm.
There are probably more, which I either forgot or don't know about. Try to get used to damping as early as possible. Try to understand when to dampen and why and how. I am not aware of any method text on damping. It is not my strong point, and I do not feel that I can help you here, except to tell you that it is important.
When your ear is trained to listen to guitar music carefully, I think you will find that you get tired very quickly of listening to a player who does not articulate properly by damping.