Bloggers make money in two ways.
1) They sell their content to different sources such as yahoo voices, aka associated content.
2) They have ads on their blogs such as google adsense.
I'm pretty sure you have to be 18, because either way you're signing a digital contract, which can only be signed by "adults"... but don't quote me on that.
Oh, and having your own website helps, but you can also use blogspot and other places. Keep in mind though, there are literally MILLIONS of bloggers out there. You have to have GOOD content, interesting content, and content that is on a subject people actually want to read about. If you're not a professional writer, chances of having a majorly successful blog are low... You have to have thousands of views a day to make ads on your page actually generate any real money.