First, you need to find a source of unpreserved apple cider. Pasteruized is okay, but be sure there are no chemical preservatives in the cider. I buy my cider directly from a local orchard which presses their own.
I have found that original specific gravities vary widely with different batches of cider. The only way to monitor is to compare initial and final hydrometer readings.
To make a simple, dry, refreshing, low-alcohol cider, boil the sweet cider in your brewpot for fifteen minutes to kill off any wild yeasts or bacteria. Transfer to a primary fermenter and let cool to yeast-pitching temperatures. Then, pitch an ale yeast. I have used rehydrated dry Edme and Red Star ale yeasts and they work just fine. Let it ferment in the primary for a week, then transfer to a secondary until clear and successive hydrometer readings show no change. Prime with 1/2 cup of corn sugar to give it a light sparkle, and bottle.
To make a sweeter, more alcoholic cider, you will need to increase the amount of fermentables in the initial sweet cider mix. A method I really like is to boil down seven gallons of sweet cider to five gallons. This concentrates both the sugar content and the apple flavor. Such a boil takes about an hour or so. Cool the must to pitching temperature, pitch an ale yeast, and follow the instructions above. Alcohol content will be the maximum that variety of yeast can stand, around 8-10%, depending on the yeast. Primimg will have little effect on carbonation at these alcohol levels. If you want a light sparkle, take daily hydrometer readings, and bottle the day you get two identical readings in a row. If you don't care about sparkle, just bottle whenever visible activity has stopped.
Other ways of increasing the fermentable sugars include adding a pound or two of corn or cane sugar (not highly recommended), honey (to make a mead called cyser), or raisins (a traditional method from New England).
To make a dry, high-alcohol cider, increase the sugar content by one of the above methods, and pitch a wine or champagne yeast. Champagne yeasts will give the highest alcohol, up to a maximum of about 16% by weight, but tend to make the resulting cider bone dry. If you want to retain any sweetness, be sure that the cider you start with is very sweet indeed. Such beverages pack quite a kick.
A nice thing about fermenting cider is that it's pretty good to drink at any stage of fermentation. I have occasionally served some unfinished by siphoning it straight out of a carboy into serving glasses.Mike Ferdinando May 31, 1995