First, I would want to know why the team has been small and unorganized. Do they have team officers (maybe flaky ones), or no officers yet? Have they tried publicizing (but are e.g. losing students to other dance groups), or not so much? Are they failing to attract team members or failing to retain them, or both?
Here are some general suggestions:
1) It's important to elect or appoint team officers. There are a lot of different jobs to do on a ballroom team, and assigning one person to each related cluster of jobs will allow much more innovation and refinement than asking the new president to do all of them himself. Officers on my team include a financial officer, an officer in charge of publicity, one who plans social events, one who coordinates with pros to teach classes, one who oversees the team-run competition, one in charge of helping out new people/beginners, one in charge of reserving space on campus, and a webmaster -- among others. These are just some ideas so that this guy can choose what is important based on his team's needs.
2) This may be obvious, but collecting a small amount in team dues will help the team provide much better quality instruction, which will help with retention, and if the amount is reasonable it probably won't reduce demand by very much.
3) The first two things will help with both organization of the team and retention of new members (#2 assuming the money is used well). If attracting new members is a problem, then improve publicity -- have a website and a mailing list, attend student activity fairs, perform at student arts showcases, post an ad on Facebook, ask team members to promote team events on Facebook, etc. I think there has been a previous thread with ideas for publicizing and marketing a collegiate dance team.