To move up to the next level, gymnasts have to meet the "mobility score," which is just a particular all-around score at a meet that allows you to move forward. An all-around score is the sum of all four (for women) or six (for men) scores received from each event.
Gymnasts compete locally to qualify for state. Again, they have to meet a certain score to attend the state meet. There are three meets a season that are designated as qualifying meets, so the gymnasts have three chances to meet that qualifying score. I think it's still a 31.0, but don't quote me on that. It's a fairly easy requirement, so most people do compete at state. Regionals and nationals don't happen until the higher levels. Once you are a level 10, you have the opportunity to participate in qualifying meets to become an elite, and again, you have to place well in order to qualify and compete as an elite. If you do qualify, you are designated as a national elite, and then I believe there is a qualification process to become an international elite. Elite gymnasts are divided into junior and senior categories by age.