First - to the GRM community:
There's a whole "culture of sponsorship" that's been fostered by the action/extreme sports/DJ/hip-hop/energy drink/youtube world. Current crop street style skateboarders are all about "getting sponsored" - they shoot "sponsorship videos" and try to get them up the chain at manufacturers. The objective seems to be having the ability to say "I'm sponsored".
Second to the original poster:
I race a C sports racer with SCCA and a BMW M3 in NASA time trials. I actually do alright in my local series in the CSR. My local Hoosier dealer (Buy your tires from Paul and Sam at Radial Tire Company in Silver Spring MD!) gives me favorable pricing, and mounts/balances/flips tires for me for free.
That's it.
Everything else is on me. And it's ~expensive~ and incredibly time consuming. I've probably got 500 hours into rebuilding the car since last season. Granted, it's a total rebuild, but it takes all my time, and a cubic mega-sh1t-ton of money. And I have a full machine/fab/composites shop at home.
In SCCA/NASA club racing the overwhelming majority do it because the love it or are hopelessly addicted to it, and can afford it.
The guys doing the Skip Barber/F2000/F1600/Playboy MX5/Grand-AM and so forth, for the most part only get a ride if they can either pay for it, or have a sponsor who's looking for a write-off of revenue.
When I was racing motorcycles a hundred years ago, I thought it would be great to be sponsored. Eventually I became good enough that a local shop was willing to pay for my tires and entry fees.
Racing was now a job. I was working for my sponsor. I ~had~ to race, and where I may have taken it easy before on an off day, I now had the commitment to place as well as possible. The sponsor and his friends hung around my paddock spot all weekend and were a distraction at minimum.
My deal with the sponsor ran through 1/2 the season, and when I put the bike on the stand at the completion of the last event, the first thing I did after getting out of my sweaty leathers was to peel off the stickers.
So, work hard, save a lot (and it is impossible for a racer to save money) and bide your time 'til racing can take place with your EXTRA money. There's a huge number of ways to have fun driving without dropping $1,000 a weekend. Autocross, rallycross, time trials, HPDE, karting, ice racing, dirt oval and so on.