BuddyPress.org

Buddypress runs as a plugin of a WordPress install, either WP single or WPMU / WP MS(WP 3.0)

If you have your WordPress install up and running then you need to upload or install via dashboard the BP plugin and activate, no further domain issues unless you have decided to run user blogs then you have considerations such as sub domains for the user blogs or sub directories and possible DNS issues if you want to use sub domains.