Make sure it runs, picks up, shifts, accelerates, brakes, steers without any major feedback or noise issues.
Go over the body and the interior for damage. For a “beater” car, it’s not a real issue, but it can be used as haggling ammo.
Make sure all the little things work, like lights (don’t forget to check the stop and backup lamps!), cigarette lighter, wipers and washers, windows/locks/mirrors (power or manual), cruise control, all of the guages (take it for a long enough test drive that you can see action on the coolant temperature guage), tilt steering, parking brake, spare wheel and tools, cabin air blower and temperature (especially important if A/C equipped), and horn.
Definitely check for the signs of water leaks, usually just check to see if there are any signs of mold or wetness on the floor of the interior, and especially in the trunk (actually check down into the spare wheel well for puddling water).
Check all of the following levels and conditions under the hood:
Power Steering Fluid
Accessory Drive/Serpentine Belts
Battery and Terminals (if the battery looks extremely shitty and is covered with this white/yellow “cake”, it likely has been in the car for quite some time and may need to be replaced in the near future).
Spark Plug Wires
Check all 4 tires for tread depth and wear. If there are only a few millimetres between the top and base of the tread pattern on the tires, they will need to be replaced soon. Check them that they are not wearing unevenly, especially on the front tires.
However, if you’re going to invest the $50-$100 to have it inspected at a repair shop, you should get a pretty good idea of it’s condition.