Homemade grape juice is healthy and delicious, but, if you've never made it before, here's some advice on the best method I know.
The first thing, of course, is to press off the fruit. If you're doing it in the professional way, you would first run the grapes through a crusher / destemmer, which removes the woody matter from the cluster and also crushes the grapes to begin extracting some fruit. And from there you press off the fruit, using a press that will give strong and steady pressure, to extract the juices, hopefully without breaking the pips inside, which are bitter. The advantage of taking your grapes to someone with professional equipment is that you will get more juice out of the same grapes, because you can't replicate the pressure at home effectively.
If for any reason you can't or don't want to use professional equipment and prefer to do it all at home, it can be done. It cannot be done with a food processor, at least not well. If you read that online, trust me, it is not a good outcome. You will grind up the pips, and you will end up with bitter juice. What you want to do instead is to break the fruit and press it off as best you can, and for this you are going to have to go old-school: feet.
You need a clean, food-safe bin you can stand in. I'd worry about the food-safe part, and I'd make sure it was clean, but you do not need to obsess about anti-microbial sanitation. Clean, but this is not brain surgery. Indeed, this is not even beer making. We usually use a primary fermenter bin--which is basically a food-safe garbage bin. You can pick up food storage buckets locally as well, and can use them afterward for storing food in the pantry. Find something that works for you and you can put two feet in. Wash the feet and rinse your fruit if it's dusty or has bugs on it, but again, don't obsess. People have done this for millennia.
Basically, to crush your fruit, you're just going to go "I Love Lucy" style and stomp the grapes until they are good and squishy. You want to break all the skins and macerate a bit.
If you have just a small amount of grape, you can pull each grape off the stem by hand, and the outcome is better. This is why professionals use a crusher / destemmer. But if you are processing a lot of fruit, this is just not real, and don't worry. You can do this with the stems on. It's just more ticklish on the toes, and it's a bit more work straining off the juice in the next stage.
For the next step, you want some cheesecloth or you can sacrifice an old sheet if you have one, which you'll use to filter the juice. Here, the process is just like making jam (and if you have a jam strainer, one of those conical ones, those are the best). But you basically need to rig up some way of straining the fruit over a container--and for the best results you want to not fiddle with the fruit when it's draining. Cover the fruit while it sits, so you don't get carried away by fruit flies, and let it drip.
This juice that flows without having to press anything is the sweetest and the best. In winemaking it's known as the free run, and it will be clear and beautiful. You might as well have a glass. It will never be this good again and will be the best glass of grape juice you've experienced--every time. Take the free run and set aside. If you're working with white wine and don't want it to brown a bit from contact with oxygen, add a little citric acid. The easiest way is a bit of lemon juice. Citric acid, though, will make your juice a bit more tart, and honestly a bit of browning isn't a bit deal. It doesn't affect quality, only colour. But by all means add some if you care about white grape juice being white instead of a little brownish.
Then you want to start pressing off the fruit in the cloth. You'll get the most yield from the fruit if you can figure out how to wring and twist the fruit in the cloth without dropping it all over the kitchen. You want to wring and wring and wring until the pulp is as dry as you can reasonably get it. Wringing and then letting it rest for an hour, and then coming back to try again will be the easiest and most effective. Set aside this juice as well, which is the "first cut" (and if you carry on the second or third). This juice will be more cloudy, but it's still delicious.
When the pulp is dry, you can put it in the compost. Or heard of piquette? You can also try making your own piquette wine with the pulp if you're feeling enterprising. We'll do another post on this shortly, and in the meantime you can look up the process on line if you're looking for more projects.
You now have your grape juice. Some is clear. Some is more cloudy. There are two schools of thought, neither right or wrong, just preference. Some people prefer to keep the two "grades" separate. Other people bung them in together at this point. As you prefer.
If you had your grapes professionally pressed off, this is also where you will pick back up in the process. You'll get your fresh grape juice and need to decide how to preserve it.
While you are thinking, keep that juice in the fridge. There are natural yeasts in your juice. If you leave yeasty sweet juice in a warm place, you will find yourself on a winemaking adventure in a matter of hours. Not the worst thing, of course. But not the juice you want to give the kids either. Keeping it chilled will arrest fermentation and let you get things organized.
You now either need to process this juice--which is to say, essentially, pasteurize it--or you need to freeze it. If you don't do something, nature will take its course, and, if the juice is exposed to oxygen, you will end up with wine (if the yeast takes over) or vinegar (if the bacteria takes over). And if the juice is not processed and not exposed to oxygen, you can make yourself sick.
So you have to preserve the juice in one fashion or another. You can--and should--enjoy some fresh in the fridge or a week or so, but to preserve it beyond that will require some intervention.
If you are pasteurizing the juice, this is basically from here a home canning project. You need to start by bringing the juice to a boil, and then you need to pressure can the juice in hot jars. For this, you want to look up and follow carefully the government regulations on pasteurizing a low-acid fruit, and I personally don't recommend this route unless you're already an experienced home canner both because there are some risks (see: sick, above) if you mess up.
I recommend, instead, the freezing route. Start by tasting your juice, of course, and making sure it's the sweetness you like. Some people like fresh, tart juice. Other folks prefer to add a bit of simple syrup to sweeten before freezing. From here, it's all dead simple. You can freeze into popsicles for the kids. You can freeze in ice cube trays, and when frozen dump the frozen cubes into a larger container or bag in the freezer, so you can pluck out as many as you need to defrost for fresh juice any morning. Or you can freeze in larger quantities in any fashion you find handy. Keep in mind that when the juice freezes, it also expands, so if you're using glass especially leave plenty of head room. We often freeze grape juice in Mason jars, because one in the fridge overnight is just the right about of juice for our family.
And that's it. You may find that when the juice defrosts it settles out a bit, especially the later pressings, where there was a bit more pulp in the juice. Just give it a good shake and enjoy. It's just the "body" of the grape.
Keep in mind as well that frozen grapes, uncrushed, are great in cocktails and as snacks, and you may want as well to freeze some of the fruit fresh from the outset. We use a cookie sheet in the freezer to freeze the grapes and then once frozen put into a larger container in the freezer. Personally, I like my frozen cocktail grapes sugared, because they are shimmery and pretty. To get the sugar to stick, just rinse the grapes in water, toss in a bowl or bag, and roll them around in sugar to coat on all sides. You do need to set them out on a towel for 10-15 minutes to air-dry a bit before you put them right onto a tray in the freezer. If they are still damp, the sugar will make puddly wet lumps at the bottom of your frozen grapes, which is not quite so pretty and looks like a Martha Stewart project that went wrong.
You can also make delicious grape pickles, which are one of my favourite Thanksgiving dishes. I spice with cloves, bay, and star anise, but you can experiment with different spice blends. If anyone wants a recipe, give a shout, and I'll pass along my proportions on vinegar / sugar / spice for the pickling liquid.