Some people don’t care if the car is a ‘heap’ as long as it starts, and gets them around town. I think it was “Drive it Forever” by Robert Sikorsky, SAE who gave this (paraphrased) technique to check an automobile engine out without benefit of trained mechanic or diagnostic equipment. This information seems more tailored to the older style domestic engines, but should prove very similar to import style engines too.
Arrange for the potential car to be “cold” - before you turn the key, it should have sat outside at least overnight. A somewhat unscrupulous seller may be sure to have the car well warmed up and running minutes before you arrive. For our purposes, that won’t work. We want to gauge how it starts cold. Check the color of the exhaust pipe. A high mileage engine that shows evidence of actual oil leakage - forget this one. A somewhat gray color is normal, black indicates as too rich condition.
Check the oil and perform all the checks as listed above. Start the car - while having a friend watch the exhaust. Does it start quickly? Does it idle smoothly? This test verifies the “cold start” health of the engine. Do puffs of blueish smoke exit the exhaust? High mileage engines often have a bit of leakdown through the pushrods and so on through to the cylinder area, this will burn off after a minute. It can be “acceptable” to a certain extent, mechanically speaking, but only for a minute.
Allow the engine to warm up for a few minutes, and then start out on the highway (if you dare!), taking it gently and easy until the temperature gage shows normal. Does the car accelerate without stumbling? Once at highway speeds on the interstate or equivalent, safely and within all applicable traffic laws and regulations, slow down to around 45ish and floor the accelerator while your now somewhat skeptical friend watches out the back, large amounts of blue smoke indicates a high mileage engine that should probably be rejected. Whiteish, acrid smoke at any point in this process indicates engine coolant being burned, a probable ‘blown’ headgasket. Another cause for rejection.
Park the car and shut it off. Attempt to start the car again, this is the “hot start” acceptability.
If an engine passes these three basic tests - cold start - highway test - and hot starting, then it will likely be a dependable engine and last for many more miles.