1. Says what would happen or be true under certain circumstances, expressed or implied. When expressed, these circumstances are rendered with the imperfect subjunctive*:
• ¿Qué harías en esa situacón?
  • What would you do in that situation?
• Me gustaría vivir en México.
  • I would like to live in Mexico.
• Yo no compraría esa computadora si yo fuera* tú.
  • I wouldn't buy that computer if I were you.
2. It serves as the past version of the future tense. Note the following pair of sentences, in which the second is a "backshift" of the first:
• Dice que irá.→Dijo que iría.
  • He says he will go.→He said he would go.
• Creemos que ellos ganarán.→Creíamos que ellos ganarían.
  • We believe they will win.→We believed they would win.
3. Expresses conjecture or probability concerning a past tense event:
• Thomas Edison sería una persona brillante.
  • Thomas Edison must have been a brilliant man.
• ¿Cuántos años tendría ese señor en 1991?
  • How old do you suppose that man was in 1991?

English "would" and non-use of Conditional
The imperfect, and not the conditional is used to render English "would" when this means "used to...":

• Cuando era niña, iba a la playa frecuentemente con mis papás:
  • When I was a child, I would go (used to go) the beach often with my parents.