Anyone can register with USEF, you can do it anually or get a lifetime membership. If you go to USEF.org, go to memberships and there is an option for join or renew. A rated show is recognized by USEF, there are C rated, B rated and A or AA rated. When you get points for a division it depends on how many people are in the class and the show rating. Schooling shows have no affiliation with USEF and unless specified points wont count towards your division, you also don't have to be registered to compete at a schooling show. A rated division is one that is recognized by the USEF and there are different finals you can qualify for, such as Marshall and Sterling, WIHS, and NAL, and your zone final. I would just glance at the rule book and see about where your mom would sign as your trainer, whether it is under the trainer or coach part, here is the online rule book, 2010 USEF Rulebook
, there are general rules and rules for specific divisions. It is confusing, especially if you haven't been around it.