Step 1: Free thyself from fear and frustration
The first thing to remember about your first RP character is that he or she is not necessarily the character you will take all the way to 70 and use to raid the Black Temple. You may very well do so, or you may not; either way, level 70 and the endgame are both too far in the future to think about right now. The primary purpose of this character at this point in time is simply to be your first stroke of finger paint on the canvas of WoW. It doesn't have to be amazing or innovative, or even "good" really. It could be all out of tune with the Warcraft lore and a mere copy of some cliched idea, and that would be okay, because after all, you're not setting out to impress the online world with your mastery of roleplay just yet -- you're just dipping your feet in the water and you want to have a good time.
That's not to say that the race and class you choose aren't important -- quite the opposite: we don't want the class and race you choose to get in the way. In fact, for your first roleplaying character it would be good to choose the race and class that you are reasonably sure to enjoy leveling with, regardless of the actual roleplaying you intend to do. The fighting of monsters is, after all, a core activity of roleplayers and non-roleplayers alike, and your roleplaying is going to be limited if you don't enjoy fighting much past level ten. Resist the temptation to try out that class you don't know anything about, since you'll have your hands pretty full with enough new things of a different sort to have to worry about strange gameplay mechanics and frustrating leveling problems.
Step 2: Chose Two Words
Having gotten some of the actual gameplay questions out of the way, the first thing actual RP thing you'll want to do is choose a very simple character description to start out with, something to define what your character is. To keep it manageable, think of just an adjective and a noun for now -- you won't be starting with any complex back-stories or complex character traits this time (and for situations where you might need some of that you can just draw on generic story material that arises naturally out of this basic character idea). These "Two Words" could be along the lines of "Playful Explorer" (suitable for any class you can imagine getting outdoors a lot), "Diligent Student" (suitable for any class you think would stay indoors a lot), or even "Hopeless Romantic" (suitable for any class). Think of your character as quite literally Level One, starting out on a new life, looking forward to have some set of new experiences and not at all sure what lies in store.
You might of course be tempted to choose a character concept like "Battle-hardened Fighter," or "Elegant Seductress" but, while those are both fine choices, they're harder to get started with than you might imagine. They don't easily lend themselves to casual interaction with other people, or naturally fitting into existing social situations. "Battle-hardened," for instance, implies that your character is gruff and not too interested in talking with people. He might prefer to prove himself in battle than actively socialize -- and after all, the RP aspect of WoW is a social one. Two Words such as "Eager Champion" might do much better to describe what you want to get at: he can still be a good fighter, but at Level One, he needn't go toe-to-toe with the first Level Thirty-Five bully to come along starting duels. In the beginning, your character should be able to duel and lose or not duel at all without it breaking his ego -- also, he needs a lot of room to grow in! By the time he gets to level 70 (or perhaps 35, even!), he will be battle-hardened enough, I assure you. "Elegant Seductress," too, could be replaced with "Aspiring People-person," someone who has come from the little town to the big city and wants to see what she can make of herself here. Call her "elegant" later on if you get a chance to socialize with finesse, and "seductress" if your character's flirting with others is significantly more meaningful than the usual "/giggle," "/flirt" and "/kiss" emotes.
The key element of these Two Words is to help you think of your character as nothing more and nothing less than a starting point, a foundation upon which you are free to grow in a number of different ways. You need this sort of character idea -- otherwise if you just say to yourself "Oh, I'll just spontaneously make stuff up!" you may get into trouble someone asks you "So where are you from?" and you don't have an answer. But if you have your Two Words ready, you might reply: "I was born right here in this little town, actually. I'm working to develop my abilities so that I can see what wonders this world has to show me! Have you been to some interesting places?" Your Two Words can help you to gradually fill out your character with natural backgrounds in WoW that fit your idea, as well as natural things to talk about that help move your character forward.
Step 3: Have a try
Armed with your favorite race and class, as well as your Two Words of character description, next just log in and meet some people. Don't be afraid to say things like "Excuse me sir, do you know where I might find a certain Morgain Pestle in Stormwind? I have these candles to deliver, you see, but I'm not sure where to find this person." Or, "You've been asked to hunt boars too? Perhaps we could work together; I hate getting to close to the dirty things, they stink so badly!" Keep trying to meet new people until you find some that you actually hit it off with. Check in now and then and try to develop the friendship your characters have just by spending time together while in character. If someone strikes you as particularly interesting, you might even approach them with a whisper using the traditional out-of-character parentheses and say: "((Hi! You seem like you know a thing or two about roleplaying...))"
The whole idea at first is to just dab your toes in the water and see if you like it, have a few experiences, and then, after a bit, see how you want to proceed from there. These three steps should help you unleash that first bit of creativity into your WoW environment. Remember to come back and visit us once you've tried them out!