Getting a domain name is the first step, if you want to continue using Wordpress.com, you will have to spend quite some money for it. You might want to try other cheaper options.
1. If you are willing to explore a little, you can setup a free site using Github.com and Jekyll, or look for any other free CMS providers.
2. If you just want to learn and experiment, try free hosting like 3owl.com and host your own wordpress site.
3. If you want to setup a professional site, and put some content up there, you can opt for paid hosting like Go Daddy or even Big Rock @ about 99/- per month and host your own wordpress site.