There are three overall types of competition – ’schooling shows’ put on for local riders by clubs, ‘recognized’ national shows (run under USEF rules), and ‘FEI’ (international) shows run under the international organization FEI (international equestrian federation). Almost all American dressage clubs put on schooling and quite a few put on ‘recognized’ (national or USEF) shows.

Riders usually ride in ‘recognized’ (national) shows for many years, moving up those test levels, and then competing for some time in the Grand Prix tests themselves, before they start to get scores that earn them the attention of the officials who select teams, and the attention of owners who have horses that could do well at the top levels. Finally, riders must compete and score well at some of the top shows in the world (FEI) in the Grand Prix tests, to get on our Olympic team. THEN! They may compete in several Olympics before scoring well enough to get a medal! It’s a long tough road!

I’m not sure what the policy is regarding membership in the FEI, but the organization that governs the US equestrian teams for international events is the USEF. I know joining the MDA wouldn’t be enough to qualify on an international level, but is probably necessary along with your USEF membership for shows that are sanctioned or run by both organizations. See if these links help you along:

USEF rules for dressage: http://www.usef.org/documents/ruleBook/2009/08-DR.pdf
FEI qualification procedure for 2008 Olympics: http://www.fei.org/Disciplines/Dressage/Documents/Dressage_OG_2008_ENG.pdf

The USEF rules has all kinds of details of how movements should be executed, legal equipment, dress code, etc as well as some qualification information.

Hope that helps at least a little bit!