One of the easiest and quickest fermented beverages you can make is apple cider.  Here's a version of what can be easily and quickly produced.  For Five Gallons of Hard Cider:
 

EQUIPMENT REQUIRED:
 
  • 6 - 10 Gallon food grade-quality plastic pail, preferably with an air-tight lid (primary fermenter)
  • 5 Gallon glass or PET Plastic jug (secondary fermenters - optional)
  • Fermentation lock & stopper for secondary fermenter
  • Plastic syphon tubing
  • Wine or Beer Bottles with closures (caps, corks, etc.)
  • Large plastic sheet or cover for primary fermenter
  • Sodium metabisulfite, iodophor, Star-San to sanitize equipment and bottles

INGREDIENTS REQUIRED:
 
  • Five Gallons Apple Juice or (non-hard apple "cider")
  • 2 tsp. Super Ferment
  • 2 1/2 tsp. dried pectic enzyme (or 1/4 tsp. liquid pectic enzyme - optional)
  • 5 campden tablets* (crushed - or substitute 5/8 tsp. sodium/potassium metabisulfite) Note: This may be omitted if the apple juice is pasteurized.
  • 1 pkg. Mangrove Jack Dried Cider Yeast (or White Labs produces an English Cider Yeast which would be perfect here!)  Some folks prefer wine yeast (e.g. Pasteur Champagne, Cote des Blancs, Lalvin B71-1122) or beer (e.g. Safale S-04 or a funky Belgian strain) yeast.
 
PROCEDURE FOR DRY CIDER:
 
  1. Pour the juice into your sanitized primary fermenter.  Add the Super Ferment and stir into solution.  If you prefer clear, non-cloudy cider, you may wish to add some pectic enzyme (2 1/2 tsp. of powder).  This won't change the flavor, but will produce a clearer final product. FYI this is the opposite of Sure-Jel.
  2. If using fresh, non-pasteurized juice (generally stored in the refrigerator): Crush up the five campden tablets and dissolve in a couple of ounces of warm water.  Stir this into the juice. Cover the pail to keep out dust and air with the large plastic sheet. or lid.  Stir the juice three or four times over the course of the next 24 hours.  This will help rid the juice of the sulphur dioxide you've just added.  After the 24 hours is up, stir one last time and add the yeast solution.  See step #3
    If you are using pasteurized apple juice (often stored at room temperature in most supermarkets.  Make sure the apple juice contains no preservatives, such as potassium sorbate or sodium benzoate. Ascorbic Acid is Vitamin C and is OK): You can proceed to immediately adding your yeast.  See step #3
  3. We've had excellent results using the Mangrove Jack Dried Cider Yeast.  If using dried cider, wine or beer yeast, rehydrate it by sprinkling into 1/2 cup lukewarm (95 - 100° F) water in a sanitized jar and cover for 20 minutes.  Add the yeast "slurry " to mixture and stir.  Re-cover the primary fermenter and allow fermentation to proceed for 5-7 days or until foaming subsides.  If you are using the White Labs English Cider yeast, simply remove from the refrigerator and allow it to warm up to room temperature before stirring into solution in the juice.
  4. While you can bottle the cider directly from the primary fermenter, most people prefer a clearer cider with much less sediment in the bottles.  For clearer cider, syphon the fermented cider into the sanitized carboy. Avoid the transfer of sediment and aeration as much as possible.  Try to completely fills the jug - into the neck (you add water or more apple juice). Attach a fermentation lock and allow the fermentation to go to completion (below 1.000 S.G.).
  5. After a couple of weeks of fermentation and settling, the cider should be stable (not fermenting) and reasonably clear.  You can speed the clarification up by placing you fermenter in a refrigerator.  Once the cider has completely stopped fermenting and has cleared up, you are now ready to bottle.  If you want your cider to be still (non-carbonated), simply syphon the cider from the carboy into your sanitized primary fermenter.  This will remove the cider from the sediment in the secondary fermenter.  Now you may syphon the cider into bottles and seal (cap or cork).  The cider is pretty much ready to drink immediately, although you will likely find that the flavor will smooth out with a few weeks of aging. 
    If you want your cider to be sparkling (carbonated): Place a cup of household sugar into a small saucepan with a cup of water, and bring to a boil.  An alternative is to place the sugar & water into a pyrex cup and microwave for a couple of minutes.  After transferring the fermented cider from the fermenter into the primary, simply pour this mixture into the fermented cider and gently, but thoroughly, mix in the sugar syrup.  Avoid excessive splashing. Now syphon into beer bottles (or other bottles intended for carbonated beverages) and seal.  Allow to age upright at room temperature for at least 15 days. Peak flavor is reached after 4 - 8 weeks, if you can wait that long. 
  6. Chill (upright) and serve. Pour carefully so as not to disturb the small amount of sediment at the bottom of the bottles. Enjoy!

PROCEDURE FOR SWEET CIDER:
 
Follow the procedure above, except after the fermentation has completed and the cider has clarified, dissolve 2 1/2 tsp. potassium sorbate and two crushed campden tablets in a half cup of lukewarm water.  Pour this mixture into the fermented cider and give it a couple of days to mix in completely.  After this time, you can sweeten the cider as you are ready to bottle.  Simply syphon the cider into the sanitized primary fermenter, and sweeten to taste with one of the following:
a) A simple syrup of sugar and boiling water: Place a cup of household sugar into a small saucepan with a cup of water, and bring to a boil.  An alternative is to place the sugar & water into a pyrex cup and microwave for a couple of minutes.  Pour this mixture into the fermented cider a little at a time.  Add syrup, stir in, and taste.  Repeat these steps until you reached the correct sweetness.  Note that it may take more than just a cup of sugar and water to reach the sweetness level that you enjoy.  Bottle up and seal.  (Hint: fructose - natural fruit sugar - works great here!).

b) For a more "apple-y" flavor, thaw out a can of frozen apple juice concentrate and mix in to taste.  For some real fun, experiment with different fruit juice concentrates (cherry, raspberry, peach, pear, etc)!  You can also use honey for sweetening.  Honey can be easily thinned out by microwaving for a minute or two.

c) Simply blend in some unfermented apple juice or other fruit juice.
Please note that without a draft beer set-up it is difficult to produce sweet cider that is also sparkling.  The potassium sorbate and campden tablets that you just added to prevent the yeast from fermenting the sweetening sugar/concentrate/juice will also prevent your priming sugar from fermenting and producing carbonation.
 
Note: All equipment should be well washed and sanitized (sodium metabisulphite, iodophor, Star-San, etc.). Fermentation temperatures should be no lower than 60 degrees F. or higher than 80 degrees F.