Feel
When you are inspecting the engine do not be afraid to get your hands dirty. Feeling the engine with your hands is just as important as looking at it. You are looking for places on the engine that are wet or greasy and these spots are not always in plain sight. Especially not when you take a look in the engine bay of a modern car, which have big plastic engine covers, like in the photo below.
Be careful: an engine can get very hot!
You can, however, easily remove these engine covers, so do not let them stop you. The cover placed over the engine in the car below was mounted to the engine with a couple of twisting. There are various types of mounting systems. So when you are not familiar with a specific type of car, ask the salesman for his assistance.