This is how I did it by the way.
1. Decide on a url address that you would like to have and register that name with a domain host. This will cost money.
2. You then have to purchase hosting space for that domain name, this can be done with the same organisation where the domain was registered or another organisation that appeals to you. Make sure your hosting contract includes access to a MySQL database.
3. You can download blog software for free from various sites.
4. Upload the software to the server where your website sits.
5. Familiarise yourself with the software and then start blogging.
There are easier and cheaper ways of creating a blog but this way you get to keep the website address that you choose and customising the blog is less limited. One day if you would like something more complete, you can delete the blog and put a fully functional website in its place.