Recently, I've heard from a few people who (seriously or not) want to "convert" to Wicca. Well, how do you do it? That depends on who you ask. Some traditions (such as Gardenarian) have special procedures and rituals.
However, eclectic solitaries (including me) will say something quite different. They'll say, that you don't convert to Wicca. This doesn't mean that you can never be part of our religion. It's just that "conversion," as far as I know, is a Judeo-Christian idea. So when we say that you don't convert to Wicca, we mean that there's nothing special you need to do. You just become Wiccan.
This doesn't mean that we'd consider anyone Wiccan if they said so. There are certain things that most Wiccans do - for example, they almost always believe in the All, the God/dess, or a pantheon. They usually follow the seasons and/or the Moon. And they never, ever are malicious with their abilities.
Some solitary Wiccans dedicating themselves will have a ceremony. Very often, they will take magickal names (e.g., Canis Fidelis).
But all in all, you're Wiccan when you can think with a clear mind, when you truly believe in at least 4/5 of the major Wiccan beliefs, and when you've done a good amount of study.
Yes, I said that nasty word, "study." But study is a central part of Wicca. Witches have been refining their methods for channelling energy for centuries, and they've been defining the official definition of Wicca for at least 50 years. It'd be asenine and idiotic not to listen to the knowledge they've given us - especially when a lot of it is as easy to get as a walk/ride/drive to the local public library. Some of it you can even get online!
You'd be surprising how easy some of the Wicca and Witchcraft books are to read. Many of them are designed to be easy for people to read, and even for teenagers to read! If you've never read any Wiccan texts, I suggest starting with two books: Teen Witch by Silver RavenWolf, and The Complete Idiot's Guide to Wicca and Witchcraft. Both of them are designed to be easy to read, and not too hard to learn - although I guarantee you won't absorb it all in one reading... ;-)
If you don't want to physically go out to get some of the Pagan books, and your parents will allow you to pay them up front (DON'T take advantange of them!) to use their credit card to order a book or two online, you can check out Amazon.com and Barnes and Noble. (Personally, my folks will let me use their card for anything reasonable I want to get online, just so I pay them up front.)
But when you're ready to become Wiccan, it'll just happen. No special conversion or Latin name required (you can take any name you want - but it'd be nice if it's a bit noble).
Even you don't become Wiccan after your study, it will open your mind. That's what Wiccan theology is all about. :-)