To transport a hero to defend or attack a Contested Zone (CZ) here are the steps you should take.
Click on your battle tab located at the bottom middle of your screen as shown in the picture above and click on the Button called "Transport Hero to a Contested Zone Controlled by your Civ". This will bring up another screen as shown in the picture below.
The 4 things that you need to do to transport to fight are as follows.
1. Select the CZ that you wish to Teleport to.
2. Select which hero you wish to send.
3. Add 10,000 Food so that you can walk into the CZ or Steeple.
These few steps will allow you to move around the map faster, To go out to plunder the enemy or to protect a City for your Civ, or even to attack an Enemy CZ.