The first thing you need to do is carefully choose a location. A muscadine vine needs 20 linear feet, preferably running north and south, with as much sunlight as possible. You are going to need a support system, and there are some options. I have tried a few, and I will give you the one I prefer.
You want 20 feet of strong wire, supported on each end by posts. I use 1/8 inch galvanized aircraft cable/rope. It is very strong but flexible enough that you can pull it straight. For posts, I use 8 foot long 4 X 4 pressure treated wooden posts. I mount the posts 2 feet in the ground and anchor them with fast-setting concrete. Let the concrete dry overnight. I then drill a hole 4-5 inches from the top of the post to run the wire through the post and wrap it around, clamping it back onto itself with 2 1/8 inch wire clamps, as shown below.
When you attach the wire to the second post, you want to pull it as tight as possible with gloved hands. If you have a second person to tighten the clamps while you pull, this is easy to do. You will plant your muscadine in the middle between these posts, directly under your wire. I have purchased my muscadines either in pots or bare-rooted while dormant. If planting potted ones, the hole should be twice as big as the pot to loosen the soil all around the new planting. If planting bare-rooted, the hold should be big enough to allow the roots to completely spread out before covering them with dirt. Once the plant is covered, I attach a vertical strand of solid core wire from the top of my support wire and push it into the ground. This will provide additional support for the vine. It’s not absolutely necessary, but I also use Blue-X plant shelters on new plantings to enhance their development and provide some protection for them. If you purchase a 2+ year vine, it will probably reach the top wire at planting. You want your vine to go to the top wire and then spread into a Y shape, with a branch going down each side of the wire. The goal for the first year is to have both branches go the entire length of the wire.