“How do you sleep after watching all the violence on TV?”

I will recommend to avoid screens 2 hrs before bed time. Avoid TV, cell phones and computer screens before bedtime.
Choose media wisely.

The obvious answer to your concern is don't watch TV prior to bedtime. Prior to bedtime listen to enjoyable music and read a good book. Lights and TV should be off at bedtime; you can leave the music on. You need to process the observed violence and all that you hear and read about; this can be done with journaling, discussing with others, or a counselor. No doubt, our daytime experiences affect our nighttime sleep.