The game has two major sections, space combat and ground combat.
Space Combat is where you pilot a ship you've acquired through the main quests or later on bought. Your ship is like a second character as it has slots to swap in and out weapons, shields, engines and so forth. Space combat itself involves flying around, targeting enemy vessels and trying to get them within the firing arcs of your guns.
Ships have 4 shield sections, being forward, aft, port and starboard, that you first have to bring down before launching torpedos to deal direct hull damage. Shields can be boosted by routing power to shields to increase their regeneration rate or by using a number of abilities that come with bridge officers.
Example: I currently have a Dhelan Warbird, a type of light cruiser, which has the following item slots:
Fore Weapons: 1: Torpedos 2: Beam Array 3: Duel Heavy Cannons.
Deflector
Impulse
Singularity
Shields
Aft Weapons
Devices: (These are things like batteries that act like health potions for shields and hull)
Engineering Console
Science Console
Tactical Console
Consoles give bonuses to shield regeneration, weapon damage and damage resistance. Impulse is your ships engines that let you move faster, Singularity (Engine for other races I believe) affects power distribution I think.
With the weapons, I can swap those in and out as I please. So you can add three beam cannons on the front and no torpedos, or as I have, a mix of beam, cannon and torpedos. Beam have a wide fire arc but lower damage while cannons have a low fire arc (45*) but higher damage.
Bridge Officers: They're the other guys on your ship bridge with you. They're NPCs that you have control over levelling. They also have skill trees that help improve their abilities (though I believe you can teach them new ones if you have the skill to). They also form your ground team.
Ground Combat:
I would liken it to Mass Effect 1 and Knights of the Old Republic. It's not strictly turn based like those two, but you can position your bridge officers by a button to set them up before combat. Different weapons have different abilities (I have a pistol and a sniper rifle) and your characters class tends to come into play more during missions. It is a bit weak with difficulty but I have been pleasantly surprised by the AI automatically doing things like reviving team members, throwing grenades and using weapons secondary firing modes.
What else... Missions:
Missions I believe are meant to be like TV episodes. So far they've been quite varied, showing off a large number of different races, different objectives and so forth. I've had a mission where I had to cloak through a turret wall to get close enough to take out a space stations weapons before fighting off other ships. There was a mission where I had to fly to a planet, fight off orbiting raiders before beaming down to the planet surface to take samples and explore. Another saw me attacking a convoy, taking out the escort before disabling and boarding the freighters.
I will say though, a bit of an issue is there is a lot of content and mechanics to understand, not to mention the UI, which the game doesn't do the best job of explaining. I would recommend keeping the
http://sto.gamepedia.com/Main_Page open while you're playing to look up things when you need to.