Exceptions- er agent.

A teacher teaches

The most important is the general rule: 

verb + er  suffix : the agent,

(person , he OR she, or a thing.)

This is the standard pattern: maybe 20 thousand verbs!

The agent MAY be a man or a woman, a person or a thing. 

In each case we will use the correspomding pronouns for the person or thing : He, him, his,

A tennis -player (person, he or she) plays tennis Nadal is a tennis player. He has won wimbledon.

Aracha Sanchez Vicario was  a famous Spanish tennisplayer  a few years ago.She played for Spain

A DVD player (thing,it)  plays dvds. This DVDplayer is a samsung. It was made in corea

A Fire-fighter fights fires
Judging by appearances (the moustache):Here we have a  man. In this case we have a fireman and he is fighting a fire  with his hose

There are thousands like these

Now  for  2 BIG exceptions 

A different word for the person:
A COOK COOKS ON A COOKER IN A KITCHEN

A few cases: the verb ends in er! to butcher

(also to father , to mother, etc)

The butcher is butchering the meat, probably at a butcher's shop!

A butcher  buys animals and big pieces of meat, butchers them, and sells the meat, This buthcher is a man .perhaps he is in his own shop, perhaps he is an employee.

Similarly

In a murder, (sutantivio asasinato) a murderer , (agente, he,or  she, ) murders (verb) a victim.

A very very very very few agents, when human, have  a special female form, usually -ess
A waiter is a man. , (or thing:  a dumbwaiter  is a trolly for food, used in hotels etc) a waitress is a human female.
This wairess is running. Her apron is blue. She has short hair under her bonnet.




we have also.
actor-actress
prince- princess
Most of the others in the dictionary are archaic.