Being shy around women sucks, doesn't it? Don't worry, you aren't the only one who suffers from this. Not at all.
But you know, you have to ask yourself this, why do you like her? If it's just for looks, forget it. If it's for the sake of a having a girl friend, you don't deserve her.
However, if you turely do like her, then another question must be asked. Would you do anything for her? Is it love, or is it just a crush? If it's just a crush, my friend, then don't make yourself go through all of this. I don't know how old you are, but trust me, crushes come and go. But, if you honestly do love her, and you really want to be with her, then there are ways around being shy.
1) In my opinion, the best way to ask a girl out, is to do it face to face. That way, you can interact with her, and it's all in all more sincere, for lack of a better word. Alas, you suffer from being shy, and it's nothing to be ashamed of. I suffer from it as well, as do many others. Because of this, number one is out.
Well, no need to fret yet. Next up, I would say is to call her. But that proposes a problem, eh? If her number isn't in the telephone book, or you don't know her parent's names, then you should ask one of your friends or one of her friends. I'm sure you can manage talking to one of her friends, as it's for a cause you no doubt want to work for. Anyway, I suggest you call her. Tell her how you feel over the phone. That way, it's a bit easier. But, you may still get shy and muffled.
If you think that will happen to you, I can propose one more suggestion. A letter. Now, this may be the easiest of all for you, but it's also lacks that personal feeling you get when you do it in person. But, it may be your only choice. So, if it comes down to this, write down how you feel about her, and throwing in a few compliments here and there couldn't hurt. Mind you, I said a few, so don't go overboard eitehr. If you know where she lives, and can stop by, write her name on the letter, and make the trip to her house. If she is home, give the letter to her, that way, it'll express your feelings without you getting all shy on her. If she isn't home, you have two choices. You can thank whoever answers, try again later and do what was mentioned above. The other choice is to give the letter to the person who answers and ask them to have her read it.
I hope this helps you, and if I can help in anyway, let me know. Also, let us know how it goes, if you can ask her out. :)