Certified GKH Gardening Expert
It is hard to know what the exact type of grape it is, but it does appear to be a cultivated, edible variety. However, just to be sure, I would take a sample to your local extension office. There are a lot of look alikes in the plant world, many poisonous.
This article will help you to care for grape vines: https://www.gardeningknowhow.com/edible/fruits/grapes/growing-grapevines.htm