formal business entity -- that is the band must be a partnership, LLC, or corporation (preferably one of the latter two), and (2) an agreement between the owners of the entity formalizing your investment (for example, a stock agreement), and (3) some knowledge of the industry in which you are investing.
LLC or corporation. We recommend that the band form an LLC or corporation because investors in those entities have limited liability. That way investors will be shielded if the band throws a TV out of their hotel window and it lands on someone's Ferrari. These entities are also better suited for making investments than a partnership. There are plenty of self help books and forms, and online programs that explain how to form and invest in LLCs and corporations, though our hearts are with the Nolo products (insert FTC disclaimer, here).
Why it matters that you learn about the industry. Every industry has its quirks and the music industry has more than most. You should take a basic primer in music copyrights and trademarks because the assets of the band are concentrated in those intangibles. You'll probably want the songwriters in the band to contribute their songwriting copyrights to the band entity. However, that's not something they're obligated to do. So, before you drop your money into the band's piggy bank, you should probably be sure that the assets placed into the entity, reflect the money-making features of the band. And of course, it's probably in everyone's best interests for you and your partner to have your own attorney and the band to have different representation. That will go a long way to prevent a post-breakup challenge to the agreement.