My mom used to use BIG squares of cheesecloth (multiple layers) and put the cooked grapes in the
middle, and roll it up and then would twist each end--actually she'd put old cut-off broom handles with the ends of the cheesecloth tied in knots onto the broom handles--so she could twist everything VERY TIGHTLY to get the absolute last drop of grape jelly out of the cheesecloth that would be strung over a big pot to catch the drips. Both broom handles would be put through the top slats of ladder back wooden chairs to hold everything in place. Just think of taking a towel out of the washing machine (no rinse cycle) and twisting it from each end with each one of your hands. The tighter you twist, the more water you can wring out.
RE the jelly--if you don't want purple hands for a week afterward, be sure to wear plastic gloves! (Mom always had purple hands after making grape jelly.)