116's primary sponsor is NASA. We receive a very large grant and an engineer

. Since we were only the 2nd NASA team waaay back in 1996 (and essentially the NASA pilot team), we went about a different way than most. Now though, you can apply for a NASA grant (
http://robotics.nasa.gov/events/firs...ication_07.php) of various types. Note that most of the NASA grants are now meant to be temporary until a team can find other sponsors to help support it, but they are often a great starting place. They are also limited, and competative to get.
When approaching a potential sponsor, treat it like many other outreach events, act professionally, and be organized.