Look at the Title before you hand over any money. Verfiy the VIN # matches between the paperwork and the VIN plate on the car. Ask to see the Sellers drivers license, to see it matches the designated owner on the title.
I usually will write a 'Bill of Sale" stating the date the car was sold, the VIN # , year , make and model. That the car is being sold "as-is" - no warranties are implied or promised. In our state the seller has to turn in a form [ removable from the title] stating who bought the car and for what price within about a week to the state DMV.
You may want to bring $1000-2000 with you. If the car checks out, you can offer give them a Non-refundable deposit, of the thousand, and ask if they will accept a cashiers check for the balance drawn on XYZ bank or credit union, which you will bring back the next day, or whenever you agree to pick up the car. Write two identical copies of a receipt for your $1000 with the VIN #, their name and address, how many days you have to bring them the balance, etc. Both sign both copies, one for each party.
Also, many sellers are willing to meet you at their house, which i prefer. You may get a better sense of the car's history/ usage by seeing it there. You get a better sense of the owner, and if they seem the type to keep up on the maintenance, have maint records, etc. Plus if something goes wrong you have somewhere to point the police towards, unlike if you just met in some parking lot.
I've found most private sellers were willing to go with the 'deposit and return with balance route'. Especially if you crawl around the vehicle giving it a good visual looking over, and respect them by arriving on time , taking it for a decent test drive and asking some informed questions about the vehicle, etc.
They can verify your cashiers check by calling the institution and supplying the serial #. - before they deposit it.
A US Postal Money Order is a valid option. If they just want cash for the whole amount, and you feel you trust the people , and their neighborhood, bring the balance back in cash the next day.
If you get a cashiers check put the VIN # or " for 2006 Model Q Honda " or similar, in the note section , or have the cashier add it to the check before they print it. Protects everyone this way.