One of the easier conjugation forms to learn, the conditional mood for the most part simply adds ~i, ~sti, ~bbe, ~mmo, and ~bbero to the infinitive of the verb.

For example, parlare becomes Io parlarei and mangiare becomes Lui mangerebbe.

The conditional mood is used in situations similar to when you use would in English to refer to potential events:

Io parlarei se avesse chiesto.
I would talk, if she asked.

Lui mangerebbe, perché mangia qualsiasi cosa.
He would eat it, because he eats everything.

Be careful to note however, that the "would" in these examples is referring to potential events. The equivalent to using "would" as a habitual past event - as in "he would go after school everyday" - is the imperfect tense.