Simple – one independant clause
Matthew took his umbrella.
We ate and slept in the same room.
The teacher spoke kindly but firmly.

Compound – two or more independant clauses joined together.
The thunder rolled; the lightening tore across the sky.
They rang the doorbell, but no one answered.
John has poor eyesight; therefore, the optometrist prescribed glasses.

Complex – independant and dependant clauses joined together.
We took the wrong turn when we reached the place where the road divided.
If you buy a camera, do not choose one that is very complicated.

Compound-Complex
Although he had many possessions, they did not satisfy him, and he longed for the happiness that others had.