How do you not take damage in a battle in Pokemon Go?

You cannot take zero damage in a fight.  But you can dodge the attacks and reduce damage taken significantly.  

While you are fighting there will be a yellow screen flash right before your opponent attacks.  When that happens forget everything else, stop attacking, and dodge.  Once you get the hang of dodging you can dodge every attack and make battles a breeze.

Remember that if the servers lag or you have poor reception, you can still take the max damage.  Also there is a time limit: you cannot dodge indefinitely.  But you can still take down a Pokemon with +200cp with ease once you learn how to dodge.

Also remember that you cannot dodge after using a charged attack.  You will take a hit no matter what.