There are hosted systems, like Blogger, TypePad, and WordPress.com, but I don't recommend them. Some hosted services are free, but others (like TypePad) can cost as much as hosting your own site.
If you're serious about making money with your blog, you'll want to have your own domain name. I recommend using free software like Textpattern or WordPress (you can research and demo a number of systems at opensourceCMS).
Since I use WordPress, I'll be talking about how to launch a WordPress blog.