I very much agree that cider is a great way to get your feet wet. All you really need to do is get a gallon of apple juice (best would be pressed apples from an orchard but certainly in these parts supermarkets or farmers markets sell apple juice. What you want to avoid is juice to which preservatives have been added but pasteurized juices are fine. Remove a cup or two (perhaps 1 pt) of the juice and add some yeast and I would say add some yeast nutrient. Removal of a cup allows the froth from the fermenting to stay within your jug or carboy.
You don't need to increase the sugar content but you can if you want. Apple juice will likely have a specific gravity (do you have an hydrometer?) of around 1.045. A pound of table sugar dissolved in the juice will increase the gravity by another 0.040 (half a pound will increase the gravity by .020), and a gravity of 1.045 will give you about 5.8% ABV (about the same as a beer) while a gravity of 1.085 -1,090 will give you a gravity closer to 11%, (If you add sugar you may need to remove a little more of the juice to provide enough room for the added sugar.
Two or three times a day I would cap the jug and give it a good shake to agitate the must- this allows air into the liquid, allows the carbon dioxide produced by the yeast to escape and ensures that the yeast have good access to the sugars.
The higher gravity must may take longer before it is as pleasant to drink as it can be than the lower gravity version but I think the lower gravity version could be clear and very tasty after a couple of months.
You could use any kind of wine or even ale yeast for the lower gravity version, cover the container with a cloth or aluminum foil until the gravity falls close to about 1.003 and then carefully siphon (rack) the cider off the lees into a clean and sanitized carboy. You could add the cup or so you held back (as long as you had it refrigerated ) to top up the cider and then add a bung and airlock to prevent air from oxidizing the cider while allowing the carbon dioxide produced by the yeast to escape.
I would let the cider clear (you should be able to read a newspaper through it if you were using a glass carboy) and the gravity fall to below 1.000. It's likely to be ready to bottle in about 6-8 weeks.
You could then check the taste (you can check the taste from day 1 - it's not going to hurt you and will give you a good idea of how the flavors change as the cider progresses) and see if you want to sweeten the cider (back sweetening) . Two ounces of sugar in one gallon raises the gravity by .005 so you can use that rule of thumb to test for the level of sweetness you want and then add that amount of sugar to the batch. BUT before you back sweeten you need to be sure that a) all the yeast has died and b) you have stabilized the cider (read about stabilization on this forum).
I wouldn't recommend that you sweeten AND make the cider sparkling as a first attempt but that might be something to think about down the road..
To make the cider sparkling you simply add more sugar just before you bottle (about 1 oz /gallon. You don't stabilize the cider and you can rely on the remaining yeast to ferment that sugar in three or four weeks. Cider ain't beer and there are no significant protein chains in the cider to ensure that a head will remain after you pour the cider but the CO2 will remain in the cider while you drink the brew.
If you choose to make a cider with a significantly higher ABV (11 %), that would need to be aged far longer IMO - closer to a year before you bottle.