Wild grapes are fairly sour if not treated with care. They also have big stones that we are not used to in our society. Those two things make wild grapes good for juice.
Gather as many wild grapes as you can when they are ripe. Green wild grapes are not appropriate for this. If you have any other berries in the freezer from earlier in the year, you can add them to the mix too. If you have any mints growing in your garden or harvestable elsewhere, that can be incorporated into the juice. A slice of lemon or other citrus fruit can also enhance the flavor. Try staying away from putting other berries or fruit into the juice if you do not know what they are.
Pick the grapes off the clusters and rinse them. A cold water rinse to get pollution and bugs off is necessary. In a pan twice as big as the amount of fruit you have, put the grapes, any frozen berries, mint and any citrus fruit you have. Cover with water so that the fruit have about 4 inches of water over the grapes. Bring the fruit to a boil one then bring down the heat to medium or lower. You do not want to overboil the fruit, but you do want to cook it. Cover the pan with a lid and let simmer for about 1/2 hour. When you check the liquid, it will have turned an amazing color. Check for taste at this point. If you find it is too sour, add a little honey, about 1 teaspoon full at a time, until it is sweet enough for you.
You will need something to strain the juice from the pulp and seeds. A metal strainer with a fine mesh will work better than trying to use a cloth. Keep the pulp for dye(hair, cloth, ect.) or put it into the compost.
If you make jelly, this is the time to add pectin for a good jelly, but I find that just having the juice is great. It doesn't last too long, not because of freshness but because it tastes good.