MSF Basic Rider Course registration varies from state to state. Contact your own state's Motor Vehicle Administration for details.
I'm an ex-MSF Rider Coach in MD. MD is getting away from centralized registration and has contracted with several Community Colleges to process registration and provide a site for training. Some registration is still done at the MVA Headquarter's in Glen Burnie.
In MD, registration for CY2004 starts in January by calling the MVA or by registering with a local community college. It is not possible to pre-register now for a class in 2004.
One option, if you find yourself with a bike and without a course registration date, is to show up on the first day of a scheduled class. Generally, there are vacancies - i.e., people who don't show. In MD, the class is filled by lottery (pick a number out of a hat) from the people who show up as a stand-by.