Lots of good info here...
Most racers have trouble asking for money from a company, and a company will ask "why should I give YOU anything". The racer now must start to think like a business man and not as a racer anymore.. YOu need to sell yourself to them, what is in it for them, what is the advantage for them. Really you are selling advertising space to them.
But as said, a lot depends on where and how you race, the big boys deal with large corporations and that is a whole different world to deal with.
If you are just a local guy and go to a few out of state races a year, and just need a few bucks to help with expenses, then it is easier, you can talk to the guy in the company direct most of the time that can make the decision.
You still need to approch them in a business like fashion. If you get some money, you need to promote their business, actually go to a lot of races, and you need to win some rounds. IF they do not see a return on their invesment they will drop you the next year.
When you watch races on tv, when the big racer wins, they always give the names of the major sponsors.
With most racers these days using enclosed trailers, they become a rolling billboard going down the road, and in my opinion, is a cheap way to advertise, givin what the advertising rates are in magazines these days.
But with so many asking for money, you need to convince them why they sould give you any. It is almost like going for a job interview, you must be prepared to sell yourself.