Depending on what the song calls for and this is a generalization, there are a few ways you can mute. Palm muting is probably the most obvious, using the thumb of the picking hand to mute unwanted strings is another and the fingering hand can also be used, it really depends on what it is you are playing. With anything new that you're learning , start slow. Get your right and left hands in sync and practice at a slow tempo to build the muscle memory of both hands. This will enable you to work on the technique you need to get the results you want. And finally, don't give up! Perserverence!