The engine block and cylinder head have many passageways cast or machined in them to allow for fluid flow. These passageways direct the coolant to the most critical areas of the engine.
Note that the walls of the cylinder are quite thin, and that the engine block is mostly hollow.
Temperatures in the combustion chamber of the engine can reach 4,500 F (2,500 C), so cooling the area around the cylinders is critical. Areas around the exhaust valves are especially crucial, and almost all of the space inside the cylinder head around the valves that is not needed for structure is filled with coolant. If the engine goes without cooling for very long, it can seize. When this happens, the metal has actually gotten hot enough for the piston to weld itself to the cylinder. This usually means the complete destruction of the engine.
The head of the engine also has large coolant passageways.
One interesting way to reduce the demands on the cooling system is to reduce the amount of heat that is transferred from the combustion chamber to the metal parts of the engine. Some engines do this by coating the inside of the top of the cylinder head with a thin layer of ceramic. Ceramic is a poor conductor of heat, so less heat is conducted through to the metal and more passes out of the exhaust.