I'll put what I'd do, but likely to get constructively corrected by one of the sages around here. I don't mean to talk down to you, I don't know where you're at so I'll try to be explanitive.
Since you already have juice....
1) Read the label and make sure your juice doesn't have any exotic preservatives. Ascorbic acid (vitamin c) is ok, but many other types will stunt and stop the yeast from taking hold.
2) Choose a fermenting vessel. I use the big blue 5 gallon water jugs for sale at most grocery stores or walmart or whatever. A bucket with a spout is useful if you're doing anything with fresh fruit, but since you're just using juice you can skip that step. You may want to get a bucket with a spout later on for bottling later on though. You can also get a nice glass carboy if you're concerned about oxygen penetrating the plastic, and this issue has been discussed at length on other threads and I've never had problems.
3) Use a hydrometer to see what the specific gravity of your juice. In general the higher the gravity the more sugar in the solution. You want a starting SG somewhere between 1.080-1.090ish for most wines. Since you're starting with regular store bought juice you'll probably need to add sugar to bring up the SG. I use this calculator thinger to adjust my gravity. Click the sugar tab and it's pretty straight forward.
4) As far as additives...
a. Nutrient: exactly what it sounds like, yeast fertalizer. I always add a tablespoon to each batch just to make sure the yeast don't get stressed.
b. Energizer: also pertty much what it sounds like. Get's the yeast going. I normally also add a tablespoon of this when I start. It can also be added later on to speed up a slow fermentation.
c. Pectic Enzyme: Used to break up pectin in fresh fruit and stop pectic haze. If your juice is clear don't worry about it. But I almost always add some when dealing with fresh fruit just to be sure.
d. Tannin: Tannin is normally found in the skins of the fruit. So if you want to give the quality of a wine that has been fermenting on the skins for a while add a bit. Most reds have this quality.
e. Campden: Adds sulfates to the solution. When added at the beginning of the brew it can keep wild yeasts on fresh fruit from repoducing and taking hold. Added at the end before bottling it helps protect from oxidation. Most yeast strains you buy are not greatly affected by the sulfates.
f. Sorbate: Added at the end to ensure that fermentation does not restart. Essential for back-sweetening.
g. Acid Blend: Increases the acidity and gives wine that charachterisitc bite. There are ways to calculate it exactly, but I normally just do it to taste.
h. Calcium Carbonate: Decreases the acidity of the wine. Important for things like muscadines that are very acidic.
5) Once your gravity is correct and you've got your additives in, you pretty much just need to add your yeast. I do so by taking some of the juice (often called "must" at this point) in a mason jar and add the yeast and swirl every now and then for about 15 min or so. Then add it back to the yeast. use a long spoon to give it a little swirl. Add a plug and airlock to the top. You don't have to worry about foam and blow-off tubes like with beer (if you do beer). It'll ferment vigorously but not messily. Make sure that your liquid comes right up to the neck of the jug.
6) Let it sit. This is often the hardest part haha. I've had brews that go crazy fast and stop bubbling in a few weeks, and others that just plug along for a few months.
7) Once the airlock has simmered down and you're saying to yourself "Hey, I think it stopped! I haven't seen that thing bubble in ages!" check the specific gravity again.
a. If it's above 1.000 syphon the wine into a new jug and check the sg periodically until it gets down below 1.000 and does not change for a few days. This process is called racking or re-racking. Be careful not to suck up the yeastcake at the bottom of the jug. I'll help your wine to clarify. You'll lose some liquid in this process (in order to not suck up the yeast cake) so have some of the original juice you used to top up the liquid to the neck of the carboy again.
b. if it's less than 1.000 and clear it's time to bottle. Dissolve 1/2 tsp sorbate per gallon, and one campden tablet per gallon in one cup of the wine and place that cup of wine in the bottling bucket. Then decide if you want to back sweeten (add sugar to make it sweeter). If you do go back to the calculator thinger and figure out how much sugar you need to make it to your taste. I normally backsweeten to 1.015-1.020 but you need to do it to your own taste. So the first time, add sugar until it gets to a sweetness you like then record that gravity so you can always hit it really easy.
c. If it's less than 1.000, but not clear, syphon to a new jug (rack), reapply the airlock and let it sit a few weeks or month for the rest of the goodies to settle out. Add juice/wine of similar taste to bring the liquid up to the neck of the jug. If you find after a few months that it just won't clear there are things you can add to aid in clearing, but this is something we can address when you come to it, plus there's numerous threads about clarifying wine.
8) Degassing. As fermentation is going on your air lock is bubbling out carbon dioxide produced by the yeast. But a healthy amount will remain dissolved in your wine. I find that if you let it sit long enough most leave the wine by the time you rack to the bottling bucket. But if you find it to be really really bubbly (and you're absolutely sure fermentation is done) you can agitate it with a long spoon, spatula, or with some sort of stirring attachment on a drill. The key thing is to move the wine without splashing or disturbing the surface much. You don't want to go introducing a ton of oxygen at this point in the game.
9) Bottling. You can buy bottles, but I get mine from the recycling at a Italian restaurant in town. Just clean 'em up nice. You can also use beer bottles and crown caps, but that makes aging difficult as gasses don't pass the cap the same way as a cork. BUT you can put a regular crown cap (beer cap) on many types of champagne bottle and lots of those bigger fancy European water bottles. Once you decide on your bottle of choice, I normally just put them right up to the spout and fill them. And to save on labels I just use a cheapo metallic marker, it cleans off easy to reuse the bottles.
I'm sure I missed something, but when you're just starting out it's a bit of trial and error anyways.