Go to WordPress.org to download the software for free to install on your own server. You'll also want to review the documentation at codex.wordpress.org for installation and configuration instructions as well as ideas for customizing the look/feel and functionality of your blog.
You'll especially want to check out all the plug-ins that are available. WordPress on its own is very flexible, and the plug-ins will expand that even more. In fact, it's possible to run an entire "traditional" website from within WordPress. I'm doing it with my own business site already and am in the process of transferring all
my websites over to WordPress. It makes for a great (free) content management system.