Here is a super easy one for you. I refer to it as "Notty Hard Cider"
This recipe will create about a 7% ABV cider that is drinkable in about a month, delisicious after bottled and aged for 3 months, and outstanding after about 6+ months. It should clear well and carbonate easily if you follow these instructions. I typically make it as 1 Lb Light Brown Sugar + 5 Gallons of Motts Apple Juice. But I scaled this down as a 1 gallon jug recipe for you to try as an easy first time recipe as you requested.
It's super easy, juice, LBS, and Notty yeast....
STEP 1 - The mix/prep - Day #1
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1 gallon apple juice +4oz Light Brown sugar.
Put this in your clean jugs and mix this up (leave bout 10% of empty space at the top for fermentation to rise)
Repeat for all 3 of your jugs.
Use 1 pack of Nottingham Ale Yeast. Open it up and put it in about 9 oz of 80*F clean water to let it rehydrate for 20 mins. Gently stir after 20 minutes to distribute the yeast evenly. This will create a nice yeast slurry. You will use 3oz per cider.
Here is a spot you can buy Notty yeast...
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http://www.northernbrewer.com/brewing/brewing-ingredients/yeast/nottingham-ale-yeast.html)
Pour 1/3 of the yeast slurry into each jug. Cap each with a stopper & airlock or even just some clean aluminum foil will work fine. You should see bubbling within 24 hours. Leave at room temp for 3 weeks (~70F). It will bubble for about 1-2 weeks. It will clear out nicely and the yeast will drop during week 2 & 3.
STEP #2A Transfer & Bottle prep @ day #21
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After 3 weeks, the yeast should be settled to the bottom of each jug. Now gently pour the cider off the yeast into a larger vessel (you can even pour all 3 in one clean pot/bucket).
*** Pouring tips: The Best way to do this is pour very slowly. Once you tilt the bottle, do not tilt it back down until you are done pouring. Do not allow the bottle to "glug" by pouring to quick, just a nice easy pour. Pour until you start to see the yeast clouding up the cider, once this begins, leave the clody stuff behind for good cider.
** Siphoning off the yeats is even better if you know how to do that, you can siphon for best results. But pouring works well for a first experiment.
STEP #2B - CARBONATION - BOTTLE PRIMING @ day 21
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Prime with 6 tsp of white table sugar per gallon, and bottle in carbonation safe bottles. Mix the sugar well into warm water and stir in very gently (2 liter soda bottles should work fine if you dont have beer bottles and caps).
STEP 3 - Conditioning & Carbonating (~day 21-31+)
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After your bottles are capped, put them in a room temp place (~60-80F) for a minimum of 1 week. Carbonation will take about 1-4 weeks to condtion/mature. Chill one and then try the bottle after 1 week, if it's not carbonated well wait another week. Repeat tasting until it's ready, leave your bottles at room temp until you chill to drink them. Save a bottle to taste at 3 & 6months, it clears well and the apple starts to shine!
CAUTION: make sure to bottle in soda or beer bottles so they can handle the carbonation. Do not bottle earlier than 3 weeks to make sure the fermentaion is complete.
Cheers and let us know how is turns out if you make it.
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