The answer is simple and complex at the same time. In order to stop being nervous, don't worry about what happens and just do it. That's all there is to it.
Lets break that down a little bit. Don't worry about what happens. Do you have problems talking to a female cashier at the mall or female relatives? Probably not. You may not be smooth and witty, but you can communicate. You can talk to them because you know the interaction isn't "going somewhere". In a similar way, if you're not trying to get somewhere with a girl, you can relax and enjoy just talking. Stop trying to sweep the girl off her feet long enough to learn to interact with women in a fun way. Once you learn this skill, the only thing that remains is learning to recognize when they're into you.
Secondly, just do it. You can't develop social skills sitting at a computer keyboard. You have to do it in person. (Chat or IM however, is a good way to slow things down while you learn how to interact in-person.) Learn to joke with girls and not take things too seriously. Serious gets boring quickly. You WILL run into situations that get uncomfortable or where things fall flat. That's a part of the growing process. Just don't be a major jerk, and everything is fine. You can be a little bit of a jerk, and everything is still OK.
One thing that I've heard that helps is going up to 100 girls at, say, the mall and saying, "I really want to get over my fear of meeting people so I decided to come up and say Hi". Listen to her response, then say "thank you for your time." If she asks a question or something you can answer, but the idea is to show yourself that approaching women is something that you CAN do, and that most women are very friendly. In the off chance that you meet one or two women who are genuinely rude, it is legitimately their problem. You'll also learn that you'll live through it just fine. For most guys who try this "exercise", they find that the first girl is palm sweating heart racing scary. The next couple girls is pretty scarry too. The next ten or so cause nerves, and by the time you get to girls 90-100 you're almost running up to anyone to get the last numbers you need to complete your challenge. If you have motivation problems, have a friend go with you, and give him $200 to give back to you $2 per approach. If you live in a small town and are afraid that people will see you again, go to a near by larger city.
The references below will likely help you at your level. If you honestly are part of the very small percentage of the population that are terrified of any talking to girls, you may have a medical condition that needs professional help. If this is the case, there is no shame in getting help.
"The Mystery Method" by Eric "Mystery" VonMarkovic
e-book at www.doubleyourdating.com