The way you compete in Fantasy Marching Arts is to apply to shows that occur during the regular season. Once you have created a group, you can click the Schedule link on the navigation bar to view the schedule for the current season (or past seasons for historical results). There, you can apply for shows.
Each group can apply for up to 7 shows per week. The hosts of those shows then decide which applications they will accept, or decline. Each group can be accepted into a maximum of 5 shows per week. Therefore, it is in the best interest of hosts to accept groups sooner rather than later to avoid being unable to accept a group that is already filled up for that week. Likewise, it is in every player's best interest to apply to shows earlier rather than later to increase their chances of being accepted.