Are your motors connected to the APM outputs as per the diagram, does pushing pitch (elevator) forward speed up motors 3 & 1 when it should speed up 2 & 4 in your diagram?
To help diagnose transmitter config issues - if you are using mode 2 transmitter..
Left stick controls:
Up/ down = Throttle
Left/ right = Yaw (turn colockwise/ anticlockwise on the spot)
Right Stick controls:
Up/ down = pitch (tilt forwards/ backwards)
Left/ right = Roll (tilt left/ right)
First thing to try is connect APM to Mission Planner using USB, power up radio and go to Initial Setup -> Mandatory Hardware -> Radio Calibration. You do not need to power the model as the USB connection will power the APM.
Then move the sticks one axis at a time and make sure the correct indicator on screen moves with it. If not then that should give you an indication which channel needs to be altered.