Step 1: Materials and a plan
Don't marry your plan. The vines will pretty much do what they're going to do; your best bet is to try to get along with them. You'll be working with three types of found wood: straight pieces (I used sweet gum and cedar) for the posts, and thick grape vines for the rails, and young vines--the longer, the better--for lashing the rails to the posts.
I chose sweet gum for three reasons: the trunks are straight and pretty strong, we have a lot of it, and we don't mind cutting it. I used cedar when I could find it already down; I won't cut down a cedar tree. Cedar, too, is straight and strong, and it smells so good when it's cut.
I worked about three posts at a time, and even then, sometimes I'd pull one up to reposition it, depending on the curve of the thick vines. Cut the posts with an angle on one end and a flat surface on the other end. That way, you'll have a pointed end to pierce the ground and a flat end to pound. Most of my posts are three to four feet long.