Use 'listen' to speak about the action of paying attention to someone, or something such as music, a lecture, etc. For example:
I'm listening to the String Quartet No. 2 by Borodin.
Pay attention when you listen to him speak.
Verb Forms: Listen - Listened - Listened - Listening
Use 'hear' to speak about an entire event or completed action of listening. For example:
Did you hear Tom's speech last night?
I haven't heard her sing yet.
Verb Forms: Hear - Heard - Heard