As others said, it can be a lot of work. We raised more in cash this year (nearly $19,000) for our Memphis in May BBQfest booth than a midsize local festival (Atoka BBQfest) raised for their entire event... but we worked hard for the money. That's not to mention $5k in beer, $5k in liquor, $20k in audiovisual setup, $4-5k in meat, etc. We hustle for that stuff and provide value to our sponsors.
1) Create a good marketing kit.
We use tiers that outline who are are, why they should sponsor us, and what they are getting for their money. Be sure to think from their point of view. I'm sure you think you've got the best BBQ within 100miles, but sponsors need to justify the expenses with one of two things.. exposure or entertainment. We even went so far as to create two kits that present the same info in very slightly different ways (varied phrasing & photos) based on if we felt a sponsor was looking for exposure or entertainment. If you're a smaller team and cant entertain at the festival, that narrows your focus.
2) Spread the word. Reach out through your network. have your freinds look into who they know. Cold call / email companies who might benefit from the exposure/entertainment you can provide.
3) Be realistic. Weber probably gets 1000 sponsor requests a year.. if not more. They have no reason to sponsor every weekend warrior out there and tend to stick to bigger event sponsorships. Target companies/individuals/businesses that are realistically going to be interested.
4) Collecting can be tricky. We have a dedicated team account with a linked Paypal account for collecting dues and sponsor payments. This allows you to accept Credit Card payments as well (minus a 3% fee), which is great for companies/individuals who may want to hide the spending in an expense account.
5) Fastest way to lose a sponsor is to not follow through. IF they're at the event, give them a little lagniappe.... something over and above. One group gets mason jars of our mustard sauce they love. Another sponsor is a scotch lover so we surprised them with a bottle of McCallan 18yr at the event for them to enjoy. Make sure you not only meet, but exceed what you promised them.
6) Follow up. Want to be sponsored again next year? Follow through after the event(s).. let them know how you did. Send them pictures of their banners on display (preferably with lots of people around so they feel like they got exposure). Show pictures of your food being prepped and ideally your accolades. Explain how you're improving on things for next year, thank them for support, and ask when would be a good time to reconnect for next year. If funds are large enough, a thank you plaque w/ good pic of your setup with their banner visible or something never hurts.
TLDR:
They key is to show value... think from their perspective on what they're getting... be clear and realistic about what you want/need... and to follow through/follow up.