I recommend contacting local businesses and asking them if they would be interested in sponsorship. Are you a non-profit or public school? If you are a public school, you are fine. However, companies usually will only provide sponsorships for tax-deductible organizations, such as a non-profit. Apply to be a 501(c)(3), then reach out to them. You should also make a sponsorship packet to send when you approach the company.
Check out this post, it was helpful for our team in gaining sponsorships: The Guide to Getting Sponsors for your Robotics Team