Look up simple facts yourself. Alt-tab out of the game so that you can open up your web browser. Most problems you'll hit during the leveling process – where to find something, what to do in a certain dungeon, tricks for an uncooperative quest – can be found on Wowhead or Wowwiki. Read WoW Rookie's guide to metagaming for even more resources.
Keep trying. We're going to go out on a limb and state the blatantly obvious: WoW is a game, and figuring out what to do is part of the fun. There's no need to frustrate yourself over technical settings or game mechanics you simply don't understand; in those situations, go ahead and ask someone to clue you in. But if you can't figure out where to find what a quest giver needs or how to beat a particular encounter, don't fold before you've given it a fair shake. Read the quest again. Look at all your spells and abilities, and consider tactics you haven't tried. If you're not sure what would happen if, then try. You'll become a better player (and have a lot more fun in the process!) if you turn the game into an exploration of your puzzle-solving abilities instead of a race to run quest parts from Point A to Point B.
Ask in the zone. Use the General /1 chat channel to ask for pointers on subjects pertinent to the zone. If you want to be taken seriously, use good grammar and spelling – no l337sp34k, plz! You're most likely to find someone who's working on the same quest and meet friends of a similar level by asking for help this way.
Pick the right person to ask. Use the /who command to look for higher-level players of your class or players who are in the zone you're having trouble with. You're most likely to find people with time to chat if you /whisper players who are traveling or in cities. The main thing to remember: don't send a random /whisper to someone who's in the middle of something requiring focus. Don't /whisper anyone who's in an instance (distracting someone at the wrong moment in an instance could literally cause a party or raid wipe). Don't /whisper someone doing an escort quest. Players who are farming for materials may be bored silly and interested in chatting, but they may have had a terribad day and want to chill out with some mindless, solitary grinding; either way, be polite.
Don't make assumptions. If someone helps you out once, don't assume they've given you an open credit line. If they've been especially friendly and helpful, ask if you can Friend them for future questions or help. If they seem uncomfortable, don't press matters.
Don't pester. If you've worked through every alternative you can think of yet are still at an impasse, don't add being a pest to your predicament. Don't whine in General chat, and don't pester individual players with repeated questions. If you can't get the answer or kill the beastie you need, move on to something else for the time being.