Greg is talking about how to tame the beast. That's what he calls his mustache. He's just using a regular comb and some scissors to trim his mustache. Beard trimming you can hide your curls and patches, whereas with a mustache you're stuck with the cuts you make. This is something you might want to do with the aid of your barber, stylist, or a trusted friend to make the initial cuts.
He sections out a third of his stache, which is mostly the curl. He moves the area he wants to maintain off to the side. Greg is gonna taper his stache but cutting at an angle like he did with his eyebrows. So he angles the comb down from the center and begins cutting. Each of the cuts only takes off about 1/16 of an inch. You can continue to take more off, then just stop when you've reached your desired look.
When you have a longer beard it's ok to take off a few inches at a time, but the mustache is meant for smaller cuts. You'll want to keep in mind what kind of line you want and follow that rule. Since Greg has a curl, he slowly works a few bits into it so it'll be feathered and a gradual look. Then he takes in the entire curl and trims a little bit of the bottoms to make the entire thing even with itself.
You can always come back the next day and fix any mistakes you may have missed. If you're going for a style, you can use a bit of wax to see what it looks like after your trim. This can also help you see any mistakes you made along the way to achieve that style. Taking a small bit off the tip also helps get rid of the split ends or dead hair.