FPS style movement controls

Hi guys, being new at this whole 3d thing I'm finding making camera movements difficult. I make slight movements but seem to either end up turning the camera away from the animations or end up making very unnatural camera movements.

I thought since I have more experience controlling 3d environments with first person shooter controls it might be easier for me to control the camera in this way.

So far I have this:

But I am having trouble finding a way of making the camera turn.
I can only seem to strafe left, right, up down, or turn the object on it's axis.

Do I need to utilise some maths here? or control more than one parameter at a time with the camera?

Any help on getting this control system, or tips on getting smooth natural camera movements would be very much appreciated.