There are a few different ways to use the word "operate"; however, the basic meaning is to do something or to use a machine or a tool.
Do you know how to operate a digital camera?
Can you operate a car that has a manual transmission?
The C.I.A. operates in countries all over the world.
My uncle operates a farm with over 300 acres. (In this sentence, "operate" means to manage.)
The doctor who operated on a man with gunshot wounds saved the man’s life.
The word "operation" is a noun. It’s used for medical procedures, planned situations, and the skilled use of machines:
The doctor performed an operation.
Several operations were necessary to cure the patient.
The military operation lasted for several days.
The operation of this machine will require some training.
A person can be an operator, but this word is usually used for a person who answers phone calls at a large company or transmits phone calls to the proper location:
The operator helped Antonio place a call to Italy.
He works as an operator.