The only way to get a "free" drive if you like is by getting noticed (for the right reasons)!
Firstly Results help a lot, you won't see many Top 20 racers at Nationals that aren't sponsored in one way or another, but usually the "A" team guys are right up there or thereabouts (you can't get away with just being nice).
Secondly is about attitude, and how you come across to anyone else. When i first started getting help i was only a kid, but my Dad was always helping other people with advice, equipment or whatever he could. I think this helped me a lot but when racing i always tried to keep a cool head, not drive dirty and wipe people out and equally talk to anyone that asked for help/advice - not acting "unapproachable" like some racers used to be (and probably still do
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Of course the other thing is that you need to pick carefully when you get to a stage when people start offering you deals as the last thing to do is pick equipment just because it's free - you are still going to pay a lot of money to race (and after all it's still a hobby to most) so don't just accept a deal if you know the kit's not up to it and won't help you improve or enjoy racing any more then currently. There's nothing worse then running a car you hate just because you get it all free, you'll end up wishing you were paying to run the car you want - trust me on that!
Most of all enjoy your racing, keep your chin up and if you continue to improve and keep the right attitue the sponsors will soon start to notice you!