I've had this discussion with my parents, though I must admit I haven't been baptized. Not for lack of want, I actually want to a great deal! Because like you, I'm terribly shy! And because I can't get up in front of the church!  But talking to your parents is the easy part. Age isn't the worry, it's your maturity. And S.E., I can definitely tell you're at the maturity level you need to be. You understand why a person should be baptized, and you've accepted Christ as your Savior. Go to your parents at the same time, and tell them you have something serious to talk to them about. Be totally honest with them, about your fears, concerns, why you want to be, and why you think you're ready. After this of course, you should always pray. If your parents feel you're ready, and you feel ready and led to do it, talk to your Pastor. Some churches make you take a Communicants class before you can be baptized, or some want you to talk one on one with the Pastor. But don't worry, it's not so bad, and you'll do fine. I feel exactly like you , and I've gone through all the steps, I just have really bad social anxiety, and having people watch makes me physically ill. So I'm a weird case there, but don't worry S.E., you have the right desire, and I know it will go fine! You're in my prayers, and God bless! 

@S.E. 

You should definitely talk to you parents about it. Don't be shy! Being baptized is a great thing. I understand that talking to your parents about this might be hard, but if you truely want to be baptized, you need to tell them, even if it is a letter. I'm sure your parents will understand. 

@BHR (and S.E.)

Depending on what type of Christain denomination you're being baptized in (Baptist, Catholic...), there are different options for your baptism. You can either be baptized in front of the whole church during the service, or you can be baptized before or after the service with just your family and other people whom you invite. So, I would look into the options your church gives.  

At my church, you go up in the baptismal and say your testimony and get dunked. Here's a draft of my testimony. It's true:

"There are many things worth living for. Friendship, love, and most importantly, knowing that God is with you. I lack in courage, and trusting the Lord gives me the courage I lack. I have been blessed with loving parents, a happy house, a wonderful dog, family, my faith, and many other thngs. This is a joyous day. My friend was telling me about her grandfather, who had three heart attacks and wasn't going to live. Her mother is a Buddist, her father an Athiest, and she doesn't know where to go. She says she doesn't think there are many gods. She thinks theree is just one. In helping her discover what she believes, my faith grew stronger."