Step 1: Equipment
1) 5 gallon bottle (carboy) - this is what you'll ferment in.
2) Funnel (the one that comes from the homebrew store has some ridges on it that allow it to have a bit of airflow around the base of the funnel - this is a good thing - if you get a regular funnel, then you'll have to hold it slightly above the mouth of the carboy)
3) 1 hole stopper (usually a 6.5 size, but get the right size for YOUR carboy's hole)
5) measuring cup
Step 2: Ingredients
1) 5 gallons of apple juice from the grocery - the cheapest you can buy - WITHOUT potassium sorbate (check the ingredients - should be only water & apples. ascorbic acid is OK, but not sorbate - sorbate kills yeast, so if it has sorbate, it won't ferment.) I usually can find it in 1 gallon jugs for about $3.50 per gallon = $17.50
2) corn sugar (dextrose) - you'll need 2 pounds. I usually buy 5 pound bags from my homebrew supplier. Table sugar works, but corn sugar ferments cleaner. You can experiement with a mix of half and half table to corn sugar, if you want. The sugar will cost maybe $3 or even less.
3) 1 packet of wine or champagne yeast from your homebrew supplier. I recommend Red Star Montrachet Wine Yeast or Red Star Premier Curvee. Another option would be Red Star Pasteur Champagne. This shouldn't cost more than $1.50.