There should be a flasher unit under the dash somewhere - usually on drivers side. It's what makes the clicking sound when the turn signals are working. It should be a small round 1/2 inch thick disk about the size of a quarter. Some plug in by or in the fuse block. If you can make the lights light on one side by signaling a turn but get no flashing - this is the most likely culprit. On some cars the 4 way flashers use this flasher unit too. Some, however, have a separate one. Good news is they are cheap! Flasher unit and location should be covered in the owners manual.