Teaching the basics of soldering, you should be able to learn how to fix broken headphones. There should be two wires protected by a covering, one which is a silvery metal and an orange wire which is your copper wire. Taking the plate for your speakers, there should be two connections where the wires belong. Using your soldering material, melt some onto your soldering gun and apply it to the two sites of the connection on your speaker plate. Place your wires on the correct areas and carefully use your soldering gun to melt the wire to the speaker. Repeat for the other side, taking care not to leave the gun on the speaker plate for too long. After you have done this, you should have repaired broken headphones to work as good as new.