Brews 1 gallon (128 oz.) of basic apple cider. You'll need more than 1 gallon of preservative-free juice to brew 1 gallon of cider. The best juice will be less filtered, from multiple types of apples, and not have acid added (because it has enough acid on its own) -- but any preservative-free juice will work.
Ingredients Step
Start filtering water -- prepare over a gallon.
PBW
bucket (2 gal.)
siphon
carboy
silicon spatula
hydrometer
graduated cylinder
black bin
Wash any grit away from the supplies.
12 ml Star San (sanitizer)
2 gal. tap water, hot
rubber gloves
bucket (2 gal.)
siphon & hose
carboy
silicon spatula
hydrometer
graduated cylinder
black bin
Using rubber gloves, measure sanitizer in graduated cylinder and mix with water in bucket (it will foam). Use siphon to transfer sanitizer to carboy. Sanitize the neck of the carboy by dumping the sanitizer into the black bin. Dump sanitizer back into bucket. Place bin on the side. Then dip each piece of equipment and place in bucket without rinsing.
4 frozen apple juice concentrate cans
10 cans of filtered water, room temp -- NOTE -- next time use 8 or 9 cans, and/or less concentrate; TBD on specific recommendations
1 campden tablet, crushed
1/2 t. pectic enzyme
1/3 t. / 1 g. brewing yeast
Stir together in the bucket. (It's okay if the bucket still has bubbles from the sanitizer.) The juice will fill more than half the bucket (these ratios make 156 ounces, which is 130% of a gallon).
Put the hydrometer in the graduated cylinder. Using the tap on the bucket, slowly release juice into the graduated cylinder until the hygrometer floats (probably around 4 ounces). Make sure no bubbles are attached to the hydrometer. Measure the specific gravity of the juice using the hydrometer -- take the reading at the lowest point (it will be something like 1.055). Make a label that contains: "Started: $todaysDate; Specific gravity: $sg" and attach it to the bucket.

Put the lid on the bucket. Put the stopper in the hole. Fill the airlock to the fill line, assemble all three pieces, and place it on top of the stopper. Put the bucket in the black bin; put both in the closet or another place that is around 50-70 degrees. Store the bucket unevenly so that all the sediment falls to the same corner.

Rinse the hydrometer and graduated cylinder thoroughly.
Check it daily. When the airlock shows ~1 bubble per minute (~7 days), start the next stage.
Carefully move the bucket and angle support to a tabletop. Connect the tubing to the bucket's spigot. Rack into carboy via tubing. Allow minimal headspace (add more juice or cider if needed). Let sit 2 weeks.
PBW
drinking bottles
siphon & tubing
bottle filler
hydrometer
graduated cylinder
Wash any grit away from the supplies.
12 ml Star San (sanitizer)
2 gal. tap water
rubber gloves
serving-size bottles sufficient for 128 oz.
siphon & tubing
bottle filler
hydrometer
graduated cylinder
Using rubber gloves, sanitize without rinsing.
Connect the tubing to the siphon and the bottle filler. (If you want to backsweeten, you can now. Fill up 100 ml in the graduated cylinder and sweeten it with stevia. Try it (on the order of 3-9 T per gallon), and repeat with different sweetening levels to decide which you like. Then sweeten the batch to that level. To make it fizzy, you can add a wee bit of sugar too; need to look into how much. Alternatively you can you simple syrup in glasses at drinking time.)

Put the hydrometer in the graduated cylinder. Using the bottle filler, slowly release juice into the graduated cylinder until the hygrometer floats (probably around 4 ounces). Verify no bubbles, then note the new specific gravity.

Calculate the % alcohol by volume as:
   (originalGravity - finalGravity) * 105 * 1.25
Rack into bottles. Label the bottles. Store in fridge to cold shock / clear the yeast. Age in the bottles.
Source: Beer & Wine Makers of America