despedir vs despedirse
Despedir is to fire someone or see them off. Despedirse is to say goodbye yourself.
despedir
To fire an employee, to see someone off, or to give off (smell, light).
Lo despidieron por llegar tarde.
They fired him for being late.
The standard word for dismissal. 'Echar' is a colloquial alternative.
Fuimos a despedirla al aeropuerto.
We went to see her off at the airport.
Saying goodbye as someone leaves.
La fábrica despide humo.
The factory gives off smoke.
Emitting something. Stem change like pedir: despido, despides.
despedirse
To say goodbye — despedirse de.
Me despedí de todos.
I said goodbye to everyone.
Always despedirse de + person.
Despídete de la abuela.
Say goodbye to Grandma.
A parent's command to a child.
Se despidió con un beso.
She said goodbye with a kiss.
How you say goodbye: con + noun.
Tricky bit
'Me despidieron' = I was fired. 'Me despedí' = I said goodbye. Learners often say 'me despedí' for 'I was laid off' and cause a puzzled look.