This page of the guide to Wasteland 3 has walkthroughs for the prologue. Our descriptions will help you complete the objectives without any problems.
The game starts on a battlefield. This sequence serves as an introduction and is not defined as a specific mission. You have to defeat the Dorseys.
The best option is to stay where you started. That spot gives you easy access to more exposed opponents. To avoid losing too much ammunition, select the targets with the best chance of hitting. Don't aim at the robot either - you will take away only a small amount its health.
In the third turn, your team will be joined by a long-range cannon. Use it to eliminate the robot. When you are determining the attack area, try to also damage nearby enemies, as shown in the image below. They all will be eliminated with one shot.
After the fight, Vera Prasad will speak to you. This conversation unlocks Welcome to Colorado quest.