You can start free blog at wordpress.com or even blogger.
If you want to make money from your blog though then I would recommend signing up for web hosting, registering a domain name and installing wordpress blogging script where you'll have a more professional blog and you'll have more control over your blog as well.
With free blog hosting you don't have as much control over your blog and can't put ads on the blog to make money from your blog.
Hosting a blog is very cheap and well worth the money spent.