No-one knows football better than the people that play and run grassroots football. Make the most of that knowledge to find a partnership with a business.
Often clubs look for sponsors of kit and equipment, this is the simplest form of sponsorship, and bear in mind that parents and friends of the players may be interested in funding a kit for the team in return for their name being associated with you.
For larger companies or larger deals, it is worth looking at companies local to you. Many companies have a Corporate Social Responsibility policy which focuses on working with their local community.
Look close to home first, your next sponsor may be closer than you think?