The most important part was to identify these as grapes as not as moonseed, which is poisonous. The leaves can look a bit different (grape leaves have serrated edges, moonseed leaves have smooth edges), grape vines have tendrils, moonseed vines do not. The surest way is to check out the seeds. Moonseeds have one crescent-shaped seed, grapes have multiple teardrop-shaped seeds.
I popped open one grape to check out the inside:
I found four seeds, each covered with red pulp (not unlike pomegranate seeds). I've rubbed the pulp off the two seeds on the left. The two seeds on the right are how they look when I first pinched the skin off.
So, feeling confident that these are grapes, I picked and picked and picked:
Then inside, I picked and picked and picked the dark grapes off the stems and the them into a pot to boil.
They look like blueberries.
I covered the grapes with water, plus another half inch. I boiled gently for 30 minutes and occasionally used a potato masher to gently press/pop the grapes. I tasted the juice and it was crrraaaaazy tart, so I did end up added one cup of sugar. I strained it all through a jelly bag into a pitcher. It's pretty concentrated and tart. Will be using some this afternoon for cocktaiiiiiils!