musicsdarkangel,
Record company people very often go on recommendations by people they know. A good way can be to focus a bit on those guys, too. Music journalists, radio DJ's, radio producers, even the guys who work down at your local CD shop is part of the chain that you wanna latch on to.
I don't know what city in Illinois you live in, but the smaller the city, the easier to get in touch with the people who write about music in the newspaper or play it on the radio. Of course, impact is all about size as well...
If you have a good sounding recording and some info/photos to go with it, check out newspapers/music mags in your area, who would be writing about your music? Invite them to your gigs (make sure you meet them before/after the gig, if possible). Send them a tape and press kit, or go to the newspaper/radiostation and drop it of yourself, a face and a handshake makes a lot of difference.
Do some research on what the music journalists/radio people you're targeting have written/done. Your local library is a good source, search for articles for example. Get to know these people before you contact them. It takes time, but it's worth it. You'll have a lot more impact on them if you prepare yourself for the meeting/phonecall/drop off/whatever.
Be careful not to just say: "Hey, do you know any A&R people at 'this' and 'that' record company?". If you're any good, that means you're also NEWS to these people. These guys love to be first - they'll donate bodyparts to be able to say they were the one who first wrote about a band.
What a lot of record company A&R guys do (as Harvey Gerst said in the link Gidge posted), is they're looking for that 'buzz'. Music journalists are buzz makers.
Also, if someone writes about you in ANY publication or play your song on ANY radiostation, it'll give you something to show to other papers/mags/radiostations/people with connections and, of course A&R people. It's the first piece or airplay that's the most difficult to get.
The first couple of times, maybe nothing will happen. Heck, it might take a year, two or four before you get anywhere. But by then everyone who 'knows somebody' will know who you are. Prepare for a "yes", but expect a "no". Some people will say you suck - don't take it personally. Come back next time and prove them wrong!! Be persistent. Watch out for when persistent becomes obstinate. Remember, you want these people to want to help you.
There are many ways to go about getting a record deal. Work on as many as possible. The most difficult one is probably to go directly to a record company without being introduced by somebody. Get to know that somebody.
Long post, sorry 'bout that.
Good luck.
micmac
I think reading is highly underrated. I'd see about books on the music industry. There might be better ones now, but one I particularly liked is called "All You Need to Know About the Music Business" by Donald S Passman. It gives a very detailed and useful description of how the business end of the music industry operates. It lives up to its title.