The conditional "would" is formed by adding the following endings to the entire infinitive verb: -ía, -ías, -ía, -íamos, -ían. (Different rules apply for irregular verbs). They are used in different ways:

To express probability, wonder, or supposition:

Le preguntaste si vendría.
You asked him if he would come.

¿Qué le gustaría de beber?
What would you like to drink?

In polite expressions:

¿Me podría traer otra cuchara?
Could you bring me another spoon?

Querría que me cortara el pelo.
I would like you to cut my hair.

To speak about present hypothetical situations:

Me gustaría que vieran un cuadro de Goya.
I would like that they see a painting of Goya.

Me gustaría que vinieran.
I would like that they all come.

In the result clause of a contrary-to-fact sentence:

Él habría jugado si ellos le hubieran preguntado.
He would have played if they has asked him to.

Yo iría al cine contigo si yo pudiera.
I would go to the movies with you if I could.