Hello! Thanks for playing, I'm glad you're enjoying the experience.
Manning turrets it's easier than it seems: you just need to get a soldier in front of the Maxim turret. Then, knee down and click either a bare hand or the purple Punch action button.
Each turn, the TUs of the soldier will be transferred to the Maxim gun, so you can shoot it. You can reload it like any other weapon, btw.