Not sure if you mean skills as in professions like leatherworking, mining, enchanting or if you mean skills as in spells and the like. My answer presumes professions.
Many WoWers have a 'gathering' profession like skinning, mining or herbalism. With those, you simply go out and gather. With each profession, you can repeatedly use a minor skill to gain experience until it turns 'grey' on your profession list in which case it no longer gives experience. As you get closer to it becoming gray, you'll also have to do a lot more of it to gain one level. Gathering professions are nice to gather materials to sell at the auction house and provide you with the income you need to buy things for your other profession which will hopefully create items of use to you and sellable at the auction house.
You can level quickly by doing a very simple task over and over again.
Take skinning: Buy a skinning knife from a general goods dealer or a skinning trainer (can be found in capitol cities by asking a guard). No matter what level you are at, you can kill very low level creatures (wolves and boars and the like) and skin them. Each one generally increases your experience. In about an hour, you can raise your level quickly to well over 50 using this method. Once you max out go back to your trainer and learn the next level of skinning.
Mining: You can get a pick from a mining supplier and learn the profession from a mining trainer (ask a guard in a capitol city). Not only can you gain a level from ores that you mine (and you can get 2-3 ores from a single mine) you can smelt the ores at a forge. Each time you do that, you'll also increase in level. You can find forges in many areas or asking the guard in a capitol city for trainers and there will usually be one very close to them.
Then some other professions: With enchanting, at a low level, you'll learn how to enchant bracers. You can re-enchant your own bracers essentially 75 times and quickly gain levels that way. You'll need the materials but it's best to find a skill or task that requires minimal materials per level of skill and do it that way. Tailoring is a nice skill to have with enchanting because at a low level, you can create items to disenchant (which also gives you a skill level) with very cheap materials using tailoring skills.
With Engineering, you can create dynamite over and over again and actually use them, sell them or give them away to friends.
In any case, I recommend looking at what is the cheapest way of increasing a level and doing that. Let me know if you really meant some other type of skill too
