Buy any apple juice that does not have any preservatives (this is important as it will not ferment if it has preservatives). Pasturization is OK. Check the ingredients, should be just juice (can be from concentrate). Ascorbic acid (vitamin C) is OK.
I have used Organic 365 (cloudy juice), tastes great, but takes a really long time to clear. I've used Old Orchard (clear juice) from Walmart, tastes great, and clears quickly. I have used cheap Flavorite Juice from Biggs, also tastes pretty good and clears quick. You can use frozen concentrate too if you want.
Shake the heck out of the juice to get oxygen dissolved in it.
Pour juice into fermenter and add yeast. I recommend an ale yeast, seems to leave more flavor than a wine yeast. Leave for a couple of months (if you can), then bottle. Can be drunk still.
I use 1 cup of apple juice per gallon for bottle priming (no sugar).
If you make beer, you can just pitch the apple juice on the yeast cake from the beer - free yeast!. Don't go the other way around and put a beer on yeast used for cider.
Most apple juice is about 1.045/1.050, and will ferment down to 1.000. That will give you between 6 and 6.5% abv.
If you want a little more alcohol, you can add some sugar. I would not add much, maybe 4 to 5 ozs per gallon. The more you add the longer it takes to become smooth. I often don't add any.
This will give you a dry cider. I like it dry and find it really refreshing when carb'd.
Simple really.