How much does a co-signer affect your interest rate on a car loan?

I have really bad credit - an early lesson learned. It is on the rebound ( I am paying off my collections one by one). I am out of school and have a ton of student loan debt. I wanted to drive my current car longer but it is giving out on me. I can't get a decent car loan because of my credit. My current car payment is $250 a month and I have no problem paying it with my income. I ran into some major financial trouble 2 years ago and was 60 days late 3 times in a row. Since then, I am out of college, have a good job... etc. Anyway, a relative has offered to co-sign for me. How do the creditors determine what interest rate to charge? And, if I pay my secured credit card bills on time, how long would it be before I could refinance to get the co-signers name off?