How does diesel engine work?

Answer 1

The diesel fuel, along with fresh air, is put under a great deal of pressure over the piston under the cylinder head. This causes the mixture of fuiel and air to explode and push the piston down. Other then that the operation between a diesel and petrol engine are about the same.

Another answer

A diesel engine works like a regular gas or petrol engine that uses injectors, except that a diesel engine uses only very high compression to cause the diesel fuel/air mixture to heat up so much that it explodes. Some diesels also have glow plugs which help the diesel fuel/air mixture ignite while the engine is cold.

A gasoline engine does not use such very high compression to ignite the fuel/air mixture. It uses a spark plug.
A diesel engine is very similar to a gasoline engine except for one main reason. A 4-stroke gasoline engine first intakes a mixture of air and fuel into the cylinder, compressed by a piston, and then this compressed mixture is ignited by a spark plug which creates a small electrical arch. A diesel engine first intakes just air into the cylinder and is compressed, afterwards the fuel is injected into the compressed air, the heat from the compression of the air ignites the mixture without the use of a spark plug.