Quick answer
hacer = to do or to make something; it takes an object.
hacerse = to become, through effort or a decision, and also to pretend.
hacerse is the change verb for professions, beliefs and wealth: things you arrive at, not things that happen to you.
Side by side
Memory trick
Something after the verb that you produced? Plain hacer. A word describing what you turned into? Hacerse with the pronoun.
Typical mistakes
Mi hermana hizo profesora el año pasado.
Mi hermana se hizo profesora el año pasado.
Becoming something needs the pronoun. Without it the sentence says she made a teacher, as if she built one.
Me hago la comida los domingos y me hago feliz.
Hago la comida los domingos y me pongo feliz.
Cooking takes plain hacer, and a passing good mood takes ponerse, not hacerse.
Check yourself
Fill in: "Después de la carrera ___ periodista."