When do you use heard and when do you use hear?

"Hear" is a present tense verb. Use it when you want to give the impression that an action seems to be happening right now:

Today I hear the sparrows singing.

"Heard" is a past tense verb. Use it to indicate that something happened some time ago:

Yesterday I heard the cardinals singing.

"Heard" is also used in the perfect and pluperfect tenses, as in the following sentences:

I hear the finches now, but I have heard them on two earlier occasions too. (Perfect)

Before I heard the finches, I had heard the thrushes. (Pluperfect)