Getting rid of your shyness will come with experience. It'll be replaced confidence and you'll look back and say, "man, I don't know why I was so afraid".
Keep agendas out ouf your head. You're probably thinking steps ahead. You're probably trying to figure out how to get this girl to go out with you. Why? You haven't said hello yet. Don't you want to see what type of person she is first? If you're just going on looks, you've got a different problem. Also don't think of her as this pretty girl. She's just another person. So go up to her and do something like, make a comment on how full the gym is that you're in together, if you're in a grocery store, comment on how rediculous the gas prices are now if you see her pumping gas next to you. That stuff will get it started. Then say, "by the way, my name is... what's yours?" DON'T USE LINES!!!
If you guys hit it off, congrats. Get her #. In case you wanna know, say something like, "I really like talking to you. I'd like to give you a call and continue our conversation. What's your phone number?" Or you could give her yours.
Later on the phone, you could ask her out. Say something like, "I'd really like to see you again. Let's meet for coffee. Are you available on ..." Or find an activity you share an interest in during the conversation and replace "coffee" with that activity. Whatever you want.
If your date goes well and you go on quite a few more and you guys fall in love. You can ask her to marry you. I'm not at that stage. I don't even want to attempt a sample proposal for you hehehehe.
Good Luck to you.