Q:

Problems with spaceships: attitude control

Let's consider DCR-97, HMSS Liberty, 300 kilotonnes (or 300 Gg) of dreadnought-carrier ship. It's a big one.
Let's say it can move forward. Let's say it could potentially move backward, or at the very least slow down. Now it would be top if it could just steer left/right/up/down without gravity-assist.
How do I accomplish that?
So we're on the same page: I guess "attitude control" is a more descriptive term than "steering", so strike any mention of steering and replace it. The question is indeed about changing the direction the ship is pointing, not the direction the ship is moving.
I'm aware of RCS though I don't know if it applies to such an heavy warship. I've heard of gyroscopic wheels, though once again, I don't know much beyond basic principle.
Requirements: Attitude control should be able to rotate the ship in any of the 3 axes in place if the ship is not moving (i.e. when docking). If the ship is moving, there is no hard requirements on turning radius, I'd just like to be able to turn left before the end of the solar system is all.
Don't forget fuel requirements if applicable.
Attitude control can also help propulsion in translation, though it isn't obligatory.

A:

How are you making it move forward? You mean accelerate, as movement is relative.  You steer by directing the thrust.  No kind of rudder will work in a vacuum.  You ought to look at information on real spaceships. 
Whatever you are doing to make the ship go, you do that off-center to apply torque as well.  Normally we are talking about rockets of some kind.
Your sci-fi ship will need some enormous power source to make it accelerate. So it will easily have enough power to feed little steering thrusters studding the ends.  If you have a made-up drive mechanism, use a litte bit of the same thing to turn.
You may have trouble with the particular design; e.g. if the main drive is a high-tech fusion reactor, but it's not practical to make tiny ones studding the exterior for turning in place, and might not be able to vector the thrust of the main drive.  Yet, such a heavy ship would have trouble using "simple" chemical rockets or compressed air for the purpose.  Perhaps the main drive, when in operation, is used to store energy somehow, and use that to accelerate reaction mass (which still becomes a consumable to ration).  You might use water for reaction mass, and produce hydrogen and oxygen from main drive power, using that as rocket fuel when maneuvering thrusters are needed.
As with modern satellites, using a flywheel saves on consumable reaction mass. But it might have to be highly advanced to handle the amount of angular momentum necessary.  Perhaps parts of the ship's mass that are used for necessary purposes (bulk stores, for example) might move relative to the rest of the ship.  

If you are asking how to control the orientation of a massive object in space, you have two choices:

apply thrust off center, thus producing torque.  To ensure you don't apply unwanted translation as well, use pairs of thrusters on opposite sides.
have a way to store angular momentum and transfer it between storage and the main body. This is done with heavy reaction wheels.

Real spacecraft that need to carefully control their orientation, like communication satellites and observation instruments, use both: the wheels have the advantage of full-time careful control without using up anything. But if corrections tend to be in one direction they eventually get "full" and rockets are used to perform the "momentum dump" of the reaction wheels.
It is also possible to use outside forces to your advantage.  Spacecraft have used solar light pressure to stabilize an orientation and kill unwanted rotation.  For a huge ship, sunlight would have little effect unless it was using something like a solar sail.

