Detailed process on buying a used car? Never owned one before?

I want a 2009 Honda Accord Coupe Ex-L V6 with navigation. I've been looking online in where I live (NY area) The range of prices I've seen goes from $13,000 - $20,000. What I don't know is what is the process on buying a used car with those prices and what APR even is. I also don't have a credit card yet only debit card. I'm 19, live at home with parents. The key part to my purchase is that there's a strong chance either my parents will buy it for me or together we will go half and half on the buying. Since I have a job. There's no way I'm buying this car with my money alone, that's just how my parents are. They want me to save as much as I can for future needs when I live my own life. So back on topic, to be on the more reality side. Let's say me and my parents go half and half on this car. How much money will I have to spend my half on for this car? Remember I wish to know how much I need to save for this baby. If this helps, my parents also clarified to me that they will pay for any repairs, maintenance, etc. All I have to pay for is gas, and personal needs for the car like new rims or whatever if I ever should do so.

Research edmunds.com. Loads of info!