how to inspect a used car for the first time when the owner is not around to give you a test drive?

Always check the gaps between the hood, fenders, doors, and trunk to make sure that they align properly and there is an even gap between them. I walk away as soon I see that one of these gaps is wrong. At this point you know the part has been removed, for what reason, who knows, but I don't care to find out.

When I bought and sold vehicles I would open the drivers door all the way then lift up on the door to check for play in the hinge. If there was play, and the mileage was low, I would suspect a rolled back odometer. Also look for excessive wear on the brake pedal/gas pedal. It is a very good idea to measure the paint thickness on the vehicle to see if any body work was done. Pull out the dipstick on the transmission and smell the fluid to see if it is burned. A compression test is very useful as well. Never buy used cars that young males owned. I preferred buying cars from older people, they are much more likely to service the vehicle. Younger people abuse vehicles.

I once was helping a friend purchase a used car, and I noticed the seams between rear quarters and trunk didn't flow evenly. Asked the owners about this and they said it had never been in an accident. I looked up the carfax and sure enough it was in a collision, so we avoided the car.

 

when buying a used car from a private party: MAKE SURE THE TITLING IS IN ORDER. You can find a car that's a deal of the century, but if something prevents you from titling (and subsequently registering) the car in your name, you're seriously screwed. You want to make sure the person selling the car actually has the right to sell the car (ie, their name is on the title), and you want to make sure things like the VIN are 100% correct (even if two characters are transposed, the DMV is likely to reject the title). The first thing though is by far the most important because you can fix the second thing with the previous owner's help. 
 
The problem is though that a number of privately sold cars in the used market are being sold by flippers, and to save (substantial) money on titling and sales tax, they'll leave the "Buyer" field on the transfer of title section blank when they buy the car and just never title the car in their name. Then when they sell the car to you, you can put yourself down as the "Buyer". No problems as long as you don't need a new title for whatever reason (VIN error, cross-out on title transfer, previous owner printed out their married name in the title transfer section when the title is in their maiden name, previous owner signed their name "Jim" when the title says "James", dog ate it, etc), but good luck tracking down the person the flipper originally bought the car from (and that's assuming the flipper didn't buy the car from another flipper). 
 
You also have to be careful of titles with multiple owners, even if the seller is one of them. Make sure all listed owners are around and will help you should you need a new title or some other DMV issue comes up with getting the new-to-you car in your name. Last thing you want to deal with is buying a jointly-owned car from a disgruntled spouse going through a divorce, or buying a jointly-owned car from a son whose dad passed away but the son doesn't have any power of attorney documents.
 
 Also, understand that some states actually have two-part titles: a "liened" title that the DMV sends to the buyer financing the car and a lien release document that the DMV sends to the bank. Once the buyer pays off the car, the bank sends them the lien release. The first part is absolutely USELESS without the second part, and A LOT of people who live in two-part title states don't even realize this (and wind up losing the lien release). So if you're buying a car from a two-part title state, make sure you have both parts OR that the title doesn't have a lien holder listed on it. Unless you're really, really incredibly lucky, a bank will only send a lien release to the person listed on the title/lien release. I've even seen situations where a bank that was listed as lien holder on a title hadn't been in business for years, and that's always an insane (and sometimes insurmountable, actually) obstacle to deal with. 
 
Finally, be careful of dealers posing as private sellers. I've seen schemes where they'll put the dealership's name as "Buyer" on the title and then give you a dealer re-assignment form (or just fill out the dealer re-assignment section on the title) with you as the transferee. The seller will swear up and down that this is fine, that they've done it in the past, and that it's completely legit, but unless you're also a dealer, it absolutely won't work. So once the DMV rejects your title application because of this, you'll be forced to go through the dealership to get the titling done, at which point they'll likely slam you with several hundred dollars (possibly up to a thousand) in various doc and processing fees. They know your only two options at that point is to pay up or spend even more money suing them. 
 
Really, the best way to protect yourself from all of this kind of stuff is to just go to the DMV with the seller and get the title transfer done before keys exchange hands.