Palm Muting
Palm muting is a technique that uses the fleshy part of your strumming hand palm to mute the strings. This creates a more articulate attack and sounds tighter. Think of punk rock and metal, most songs would be terrible without palm muting.
When palm muting, try and keep it closer to the bridge. Focus on the lower strings. You may want to use an amplifier with some high gain to find the sweet spot. Experiment to find what works best for your style.
Left Hand Muting
Left hand muting is great for muting specific strings or everything at once. Just think about when you first started, you play a C chord and all the open notes just buzz or don’t play at all. Learn how to harness this skill to your advantage. That way you can strum away with chords with open notes, and you mute them with your fingers on your left hand. For instance, you can wrap your left hand thumb around the neck to mute the low E string. Again, experiment to find what works best for your style.