Im not sure about how we find sponsors...
but I do know that we choose 2 schools we want to sponsor, go to them, show videos of the previous years, demo our robots, answer questions, explain that its more than just mechanical hands on stuff...ya know, make it interesting to everybody.
If they decide that they want to join FIRST, then we will go over every monday of the build season and help them out with whatever, and we also invite them to our shop and supplies whenever. We give them our room phone number and email incase they need us. We also point them towards resources, such as CD.
To top it off, some of our team members go out on Friday night for ice cream our whatever, and we will invite them along too.
Hope that helps!