Give a company a call, you'd be surprised at how easy it can be. But think of it as a job interview. And if you don't do a ton of shows, don't bother, they won't care. We've gotten turned down a lot, but if you don't try, you'll never know. If you're car isn't already heavily modded, then the bigger companies won't want to help you. Best bet is to find smaller local shops to sponsor you first. That way you'll have some history when you approach the big names. My car and my girlfriend's Integra are both heavily sponsored, but they expect us to be at a lot of shows and provide them with a lot of exposure. It's not just getting free parts.
Having said all that, if you manage to get a magazine feature agreement, then call up every company you can think of and work them for parts. They'll almost always say yes if you have a deal for a magazine feature.
Right now between my girlfriend's car and mine, we have
AEM, Alphasonik, Corbeau, Dynamat, Holley, Infinity, JBL, Katzkin,
Meguiars, Nitrous Express, NOS, Vitek
and right now we've got pending deals with RO_JA for wheels and Autometer.
All of those listed sponsors provided parts, mostly free. Some at a very, very steep discount.
There are also a bunch of smaller shops that provide labor or random parts for the cars. But it's a full time job just meeting all the sponsorship obligations, they say you have to be at a show, you'd better be there.
We're trying to get to the next level of sponsorship where the companies pay for our travel expenses to shows, as well as giving us the product.
My car
http://www.evolution-autodesign.com/projects/maxima.htm
Hers
http://www.evolution-autodesign.com/...ts/integra.htm
And right now both cars are undergoing extensive bodywork/full stereo rebuilds/and a ton of interior work. The cars have to be kept unique and very eye catching to keep sponsors happy, sometimes they even tell you how they want you to install their product (usually stereo companies)