Step 2: "The Hook"
This is half the battle right here. You're not the most suave guy, and you want someone to notice you. Guess what, I am not going to give you cheap tricks, or cheesy lines.... infact I am of the personal belief that if its a line at all, its cheap. The best contact comes spur of the moment, not necessarily some heartfelt speech, but most likely a comment, or a joke or a witty interaction based on the situation.
-Approach a girl who doesn't seem to want to be approached
-Approach a girl in a bar, or club--these girls are looking to be wooed by a fast car, cheap haircut, and lame lines. They have their guard up, and don't want to be bothered.
-Try to hard. This is the biggest game killer ever. I can write pages on this, but I'll put it at this "if you're frustrated--you probably trying to hard, if she's frustrated--your definitely trying too hard"
-Place yourself in a situation you are comfortable with
-Give yourself any social edges possible
-Not rule out friends as possible romantic interests
-Not rule out the idea of meeting someone in the strangest places
-Act confident and natural
Conversation is after all the heart of getting to know someone. "First contact" is the most important. If you can keep someones interest and make them laugh, and feel good about themselves, you've got someones interest, and can take it to the next level... phone number, going on a date, etc. There are some things to avoid during conversation, for instance you want to avoid any serious subject... war, politics, religion, abortion, etc. If one of these does happen to come up, keep it light, and change the subject matter. Also you want to avoid complimenting her too much, this comes across as desperate/needy.
Be interested in her personality, be genuine, try to get to know her. talk about your common ground, get her talking about what excites her, what her interests are. Do talk about yourself, do be polite. Don't ramble on about yourself, this can happen if there is a gap in the conversation it only proves to makes this awkward. As a general rule of thumb a girl will ask you if she is interested to know something about you. Pay attention, don't just hear, listen. Make a mental note of things she says, remember them, there will be a quiz later.
You want to keep your body language in mind too... there are far better resources on body language than this article, and I strongly suggest you look into them. Mainly you want to keep a firm grasp on what you are saying with you body. Keep a good posture, relaxed but not slouching. Don't let your eyes wander too much, be confident and look her in the eye when speaking to her. Mind your hands, don't let them fidget and play with something (tablecloth, hair, keys, etc). Don't move too much, nervous feet shuffling, shifting your weight. Act casual, and try to keep your actions on your mind so that you don't let them get the best of you.
Generally treat a girl the way you would like to be treated, be polite, considerate, and genuine. It seems like common sense, and it really is, but alot of people forget that, or overlook it. Try to keep that in mind.