The website to check whether the car is on a loan, or stolen, is:
www.revs.nsw.gov.au
You'll need the rego number, owner's name, and maybe the engine and/or chassis number.
It may seem wise to get the NRMA to inspect the car, that way you don't end up buying the car and discovering it has a $1500 fault, or two or three.
Anyhow, when you have bought the car, get the guy to sign the transfer form on the back of the rego papers. Also, go into word and make a receipt kinda thing, and get the guy to sign it and print his name, date, etc, just to cover your arse. I made one for when I bought my car, but it doesn't looked like I saved it (sorry).
You'll need to go to the RTA within a fortnight of buying the car and transfer the rego into your name. The transfer fee is about $32, and you'll need to pay stamp duty (tax) as well, which depends on how much you paid for it. Don't forget to get insurance before you start driving (3rdP Car and Property, 3rdP Fire and Theft or Comprehensive), otherwise you're screwed if you hit someone. It's also cheaper to register your car in one of your parents' names, and also have them as the main driver on your policy with you as a nominated driver. You'll pay a bit less on CTP Greenslip and your normal insurance cover.
It also helps (trust me) to be a member of the NRMA. The car will break down eventually - all used cars do - and it'll be at the worst possible time. Being able to call the NRMA and get them to come and help you is very reassuring; especially when you DO break down, not IF.