Things you should know before going to check a used car

When buying a used car, without a doubt, first check a car history records. Some cars may have been flooded - worthless to buy. Others were written off by insurance due to serious accident. Many cars have altered mileage, and so on.
Follow this link to learn more How to check a used car VIN history report
If looking at the used car you noted any problem with the engine (e.g: major oil leak or strong noise) or any abnormal behavior don't let the salesperson to mislead you. They may tell you, for example, that the leak is "overflow from the recent oil change" or "the noise will disappear later by itself or something like this". Generally, such defects never disappear by itself. If you have hesitation, move on - there are so many cars available.
Ask for service records if they are available. Look for oil change intervals - was the oil changed regularly? I mean driving 1,000 miles over suggested oil change interval won't cause a big damage, but, for example, 9,000-12,000 miles (15,000-20,000 km) without an oil change may cause serious engine problems in the future.

How to check the oil

Park the car on a level spot, turn the engine off and set the hand brake. Locate the engine oil dipstick, pull it out, wipe it off with clean cloth and insert it back. Pull it out again and have a close look. If you've never checked the oil level before, follow this link for detailed guide How to check engine oil.
If you find the oil is completely black (although for the Diesel engine black oil is normal) and (or) the oil level is very low (left picture) - suspect excessive oil consumption and (or) lack of maintenance. In either case the engine will more likely to have problems in the future. Another sign of poor maintenance would be dark stains (carbon deposits) covering the oil dipstick along its length.
Well maintained engine will more likely to have cleaner oil and the proper oil level (right picture), although this doesn't necessarily mean that the engine is in good shape; the oil just could have been changed recently.

If it's possible, look at the internal parts through the oil filler neck (Don't open the oil cap while the engine is running!)

Dirty engine Clean engine

Oil sludge inside the engine

With the engine turned off, try to open the engine oil cap and look inside through the oil filler hole. Use a small flashlight. If it's possible to see any internal parts there, check their condition. What you are looking for is the oil sludge - this thick black buildup on internal parts you can see on the lower photo (this is how the sludged up engine looks inside, with the valve cover removed). If you see a lot of black oil sludge buildup inside the engine it means that either the engine oil hasn't been changed for a long time, or the engine has been overheated, or poor quality oil was used.
In either case, avoid buying such a car - sooner or later it will have serious engine problems.
Well maintained engine usually looks pretty clean inside; if you check few cars of the same model it's easy to see the difference. However, again, if the engine looks clean inside it doesn't mean that it has no other possible problems - as a last step, have the vehicle inspected by a mechanic of your choice.

If you find evidence of badly made repairs, avoid any such car.

If you find evidence that the engine has been repaired with inaccuracy (too much bulging of gasket maker, as in the image, loose bolts, stripped treads, altered wiring, broken fastenings, missing bolts or covers, etc.), avoid buying such a car because quality repair is possible only by very skilled mechanics. Just imagine how the engine has been repaired on the inside if it looks this way on the outside?