The easiest is pinning them. Dig a little trench, lay a shoot in the trench in June or July, cover with dirt, and clip it loose from the mother vine either after it goes dormant or just before coming out of dormancy in the spring. It can be dug up then or the next fall. When you cover the shoot with dirt, leave several inches of the tip end sticking out of the ground. You can pin it down with landscaping pins like they use to pin down that black landscaping cloth. They look like a big, long legged staple. Or put a brick over it. You are almost guaranteed to trip over it and yank it out of the ground if you're like me.
But I have better luck air layering. Here's a u-tube [ame]https://www.youtube.com/watch?v=uFlsrU15uoc[/ame]
which shows how. One advantage with air layering is that you can see the roots in the bottle and if you're careful you don't have to cut or tear the roots off when you plant it. Muscadines will grow backwards or forwards in case something unfortunate happens with the tip end. If you're serious about this or have the materials handy, the best rooting soil for the bottle is 1:1:1 sand, pine bark nuggets, peat moss.
They can be propagated from cuttings with a misting bed.