Combat is fairly 'tame'
Person-Person combat is very simple; Hit a creature (or low armor spaceship) with a melee weapon. If you hit the (sometimes hard to get) hitbox, your attack will be checked against their agility, then against their defense, then they get damaged. In the later parts of the game, you get Power Armor, which almost entirely removes the threat of creatures, and makes melee weapons near obsolete. You can also use a ranged weapon (rifle, pistol, etc) which is pretty much the same, but with ammo limitations, and a longer range.
Ship-ship combat isn't really fast paced and dogfighting on any level above fighters. (which aren't used much, but can still be of use occasionally) You have the Turrets, Weapon Bay, Armor, and Shields. Shields are managed at the shield console, and you can distribute shield power to different areas of the ship. (something like this, I believe. I haven't had much experience with the shield console.) Turrets are placed anywhere in the ship, and are automatically crewed by soldiers. They do minor amounts of damage, and have the ability to aim. Their use varies. Sometimes used against fighters, sometimes against ships. You choose a ship's armor level in the design, and it affects its armor level against attacks. Higher armor ships can sometimes completely ignore attacks by lower level ships. Weapon Bays are the most important part of ship to ship combat. There aren't any varieties of the combat version, but it's still useful. The weapon bay is a room in the ship with weapon modules, which add to the power requirements, and other stats of a single shot. You choose a target in range at the Weapons Console, press fire, and if they're in range, you have enough energy, etc., the ship will fire and make damage their shields/hit their armor and if high enough TL, will pass through and damage a random system of the enemy ship.
The Ship to ship information may be a tiny bit inaccurate at points, and I recommend you use the information for only a general outline. Hope this helped.