Growing a Grapevine?

First, check with your local nursery to make sure you are in an area where grapes will grow. They will also advise you which varieties are best. When I was a child in Illinois we had a concord grape vine in our back yard which did produce grapes.
Now I have one in my yard in Santa Clara county in California which is also doing very well.

Next, plant it somewhere that you can have a very good trellis. Mine is made from 2x2s and leans against the side of the house.

It supports the almost 100 lbs of grapes every year without falling down. That is just from one plant!

You could also train the vines horizontally along a fence. Every Fall we prune the vines way back to just the thickest ones. It might be a good idea to go to the library and take out some books about growing grapes or buy one at that local nursery.