The most basic strategy in starship combat is to maneuver your ship and use your energy weapons to bear on one section of your enemies shields. Knock those shields down and then use your photon torpedoes on the exposed hull.
Here are the three basic types of starship that you can get on Star Trek Online. The first one is a Cruiser. Cruisers are really tough. It takes alot of damage to take one of these ships down. Cruisers have alot of crew so they're hard to disable. This is really good for tanking.
The second kind is an Escort, Escorts are really fast, pretty manoeverable, they can inflict alot of damage at one time but they're pretty weak so Escorts are alot better for dealing DamagePerSecond.
The third kind is a Science ship which is really good at increasing the abilities of you and your teammates and for decreasing the abilities of the enemy. They can do crazy stuff like bouncing stuff off the deflector dish or scrambling enemy sensors. Science ships are really good at doing support.
One of the additional ways you can customise your starship, instead of just customising your crew, is to customise the components that are on your ship. So for example, you and I may have the same class of ship but the items that I've put on my ship may be different than yours. Take for instance, some of the station modules that I've put on my starship may impact on my phasers or photon torpedoes. There might even be a difference in your deflector dish, so some of your bridge officer powers (which you've also customised.) may act differently depending on the gear you've put in your ship even though I have the same class of starship.
The proper configuration of your ship's equipment and crew will prevent you from becoming a sitting duck in space. Its really the weapons, deflector dish, impulse engines, the consoles that you install in your ship as well as the bridge officers who are activated at that time who really determine how well you play in combat.
Bridge officers in Star Trek Online change how you play the game. You actually select them, train them up, give them new abilities, they can learn abilities from new Bridge Officers and they actually affect your powers that you have access to in space. For instance you can have Engineering Bridge Officers that are really good at fixing your ship or making it go faster. Those are the ones I tend to pick, so that I can be a bit more durable and have some escapability. You can also get Engineering Bridge Officers that will give you extra power to your engines or your weapons. Tactical Officers will allow you to fire multiple torpedoes at once or really overload one phaser and shoot one giant beam of energy.
Science guys let you mess up your enemies sensors so they can't target you confusing who they know whos a friend or a foe or boost your friendly ships, making their shields better and enhancing their sensors. We are the Borg. Resistance IS Futile.
Play Long and Prosper, Trekkies.