Pickpocket has to be one of the easiest skills to level. Just by pickpocketing your level increases rapidly. For other skills you have to spend money to level them, find the right ingredients to level or have to use the excessively, this is not the case with pickpocket. Not only is it free, if you have the right perk you can sell the items you pickpocket to vendors and make a fair profit.
As I said above, all you have to do is pickpocket items. From experience I find that not everything you pickpocket rewards you with the same experience. Because the success of a pickpocket attempt is dependent on the weight and worth of an item, I assume that the experience you gain from pickpocketing an item also depends on those factors.
The items I pickpocket I usually use to level the enchanting because enchanting requires a vast quantity of items to enchant. After that they are usually worth much more than when they were unenchanted. Thus selling them is even more profitable. If you have the right perk in speech you can sell stolen items to vendors, but speech is very slow to level up so what you will want to do is join the thieves guild and do their quests until you receive the thieves guild armor. Then you can sell any items, even stolen items, to the lady that gave you your thieves guild armor, although other vendors offer more money for the same item.