A few weeks ago, I got ahold of a TON of locally grown grapes and decided to attempt to make my own grape juice. I used this process and it was surprisingly easy, even though it did take two days.
The first thing I did was to take the grapes off of the vine, clear out any stems and then wash them. Then I used a potato masher to crush them since I don't have a juicer.
I let them simmer for about 10 minutes to loosen the skins and then strained them. I just used a regular mesh strainer and not a cheese cloth as recommended. It worked just fine. At this point I let the juice sit in the fridge overnight before I further filtered it with a coffee filter (which didn't work!). I didn't can the juice because I intended to drink it right away. I wound up diluting it with a cup of water because it was pretty strong for me. But, it was so good!