1. To express a hypothetical action, either present or future.

• Ahora mismo me comería un donut.
  I would eat a doughnut right now.
• Mañana te daría el dinero (si lo tuviera).
  Tomorrow I would give you the money (if I had it).

2. To express a future action with respect to a past action.

• Ella dijo que vendría hoy.
  She said she would come today.
• Mi vecina juró que nunca volvería a beber.
  My neighbor swore that she would never drink again.

3. To indicate probability or conjecture in the past (like the future of probability, but with respect to the past):

• ¿Dónde irían los chicos anoche?
  I wonder where the boys went last night.
• No sé, estarían con sus amigos.
  I don’t know; they probably were with their friends.

This idea can also be expressed with probablemente and the imperfect:

• No sé, probablemente estaban con sus amigos.
  I don’t know; they probably were with their friends.

4. To soften a request or statement in order to show politeness:

• Quiero más té.
  I want more tea
• Querría más té.
  I would like more tea