So this is what we did when we bought my daughter a car.
She found one she liked in an ad and we contacted them for a test drive. Did the test drive and she wanted to get it. We then gave the sellers a $100 refundable deposit (personal check) to hold the car for us for 1 week and scheduled an inspection at a local Ford dealer and coordinated this with the seller (we paid for the inspection). We also signed paperwork I typed out discussing all this, including driver's license info for both parties, and we each kept a copy. On the inspection day, the seller's dropped the car off, we showed up at the same time to sign some paperwork and the dealer went through it with a fine-toothed comb...we were surprised how thorough the inspection was. In the end, this car, which by all accounts so far seemed to be in great condition, needed $12,000 in repairs (on a $7,500 car). We met the sellers at the dealership when it was done, went over the findings and walked away. We let the sellers keep the inspection report and we got our $100 back, but we were out the $175 inspection cost.
Next week, same exact process except it was different sellers and a Nissan and we went to the Nissan dealership. This time, it passed with flying colors and she decided to go through with it. Sellers gave us back our $100 deposit and we set a date to meet them at our bank because my daughter was getting a loan. We all showed up, both parties signed a bill of sale amongst other paperwork the bank required, they took the title and gave us the papers to take down to the DMV and register it and we called USAA and put an insurance policy on it. As for the money, the sellers had their bank information and our bank just did a wire transfer to their account. Simple.
Hope this helps give insight on how to go about it.