Use the Experience Point (XP) resource to train your survivors to a new level and don't forget to upgrade their gear as well.

Survivors can be trained at the Training Grounds. Tap on the building to select training, then make your pick. Training requires time and resources, or you can speed it up by using Gold or Speed-Up Tokens. Survivors will be unavailable for missions during training and injured survivors can not be trained while healing.

Weapons and armors are upgraded at the Workshop. Tap on the building to select the tools icon, then select your desired piece of gear. The equipment is always divided by survivor class so you can find it more easily. Upgrading gear works in the same way as training survivors.