My wife checks every button, window, seats, lights, sun roofs, interior etc.
I bring a floor dolly and roll under the vehicle and check for rust, damage, CV boots, leaks, muffler etc.
Go over the outside with a fine tooth comb, look at top.
I drive and test all shifting, 4WD, Hi/Lo etc.
If it's not a Toyota dealership, I put a deposit and negotiate to have them pay for an inspection.
If I can't negotiate that, I pay for it myself and take it to a dealer. They'll inspect it for less that $200. Money well spent IMO.
Run the VIN number to check all maintenance, warranty work done etc.
You can check tire wear by usually looking at the spare. I put a quarter in the thread on a new spare, then check against tires on the road. That will give you an estimate of when you'll need to spend another $1000 on tires.
Drive expressway and around town.
They fix anything that's wrong at Toyota.
Best I can do to avoid issues.