A game engine is generally consider the code that can be pulled out and replaced with out changing the game it self.
Like has been stated already, how exactly you USE the code of an engine depends on the engine it self.
Commonly, you will instance class from the engine library and use them. The way you do this will be dictated by the engine.
Some might provide more features then other, some focus on module-ness.
Often an full game engine, will just tie together various sub engines, such as a graphics engine that handles actually drawing to screen. A physics engine for simulating your game world. a UI engine for the UI and menus. a network engine that handles entowrking things.
The 'game engine' may well have these components built in directly, or it may just be wrapping another engine/library so that you use it in a similar way to the rest of the engine.
