Start preparing early. Not only will this give you time to find more scholarships, but it'll give you time to prepare your audition.
Look for music scholarships at the colleges you're applying for. These will tend to give the highest amounts of money with lower competition pools. Usually, these scholarships will be well-advertised in order to draw strong talent, but don't be afraid to ask about what you might be seeing. Don't just ask the admissions counselor, but find someone in the music education department (this can also double as an opportunity to find out how well-connected your potential lesson teacher is to the goings-on at your college).
Look for independent scholarships for musicians. There are hundreds of foundations, non-profit organizations, and institutions that support young musicians this way, and there's no limit to how many of these you can apply for and use if you win. If you decide to double-major in performance, search also for performance or general music scholarships intended for your instrument, especially if you play an instrument that tends to fare poorly in open-instrument solo competition, such as low-voice instruments.
Choose the scholarships you want to apply for. Although applying for as many as possible can increase your odds of winning money, nearly all scholarships require a live audition and/or audition recording, so be aware of the danger of spreading yourself too thin. Instead, pick a few scholarships based on the likelihood of winning, the time you have to prepare, and the potential winnings compared to the difficulty of preparation. Look especially for auditions requirements for different scholarships that can be fulfilled by preparing the same pieces of music.
Get a calendar and use it. Mark down all application and audition deadline dates right away with each new scholarship you find. Marking them somewhere where you can see them every day, like a chalkboard or dry-erase board, is also a good idea. It's easy to lose track of these, and that's not a risk you want to take.
Read the application materials and instructions for each scholarship carefully and repeatedly. Missing even one or two small instructions can be enough to disqualify you, even if your audition or recording is spectacular.
Practice for your audition. When preparing for an audition, increase your daily practice time by at least 50%, and don't neglect your fundamental skills. Frequently practice playing your audition music as you would in an audition setting; play everything through in the correct order without stopping or repeating. Do this alone and for other people.
Make any audition tapes using high-quality equipment. If you can't enlist the services of someone with pro equipment, set up a home studios using a minidisc recorder, digital audio recorder, or other similar medium. Remember that the quality of the microphone you use is more important than the quality of the recorder itself. Record in an acoustically dry, quiet space, such as a church sanctuary with carpeted flooring, a large basement, or your band room after school. Record all tracks for one audition in the same space.
When auditioning live, pay attention to your personal appearance and conduct. Dress neatly and well, avoid revealing clothing, and be as polite as possible. Make sure to be well-hydrated and bring along a bottle of water, just in case. Be as polite as possible. If auditioning makes you nervous, eat bananas on the morning of your audition (they contain natural beta-blockers) and take time to breathe deeply and slowly through your nose.