Newbie: powering and controling a motor - 12v
Answering only electronics part:


  With this motor (link below) it is as simple as wiring in a positive
  and negative wire with a switch?


If the motor has to stop after 90degree rotation of the plate, you should having feedback mechanism.  Feedback (depending on how much accurate the tilt has to be) can be through:


rotary encoders
stall current
Reflective sensors
angle inclination detection using another circuitry


Stepper motors can also be considered which can deliver precise rotations every time. Depends on the precision.


  rotate it to the desired angle and then switch polarity for the
  opposite rotation?


Yes. You can look for H bridges which will reverse the polarity of the motor. Depending on the drive current of gear with maximum load, the available supply and space the H Bridge elements can be chosen. Also, you can go for IC solution.


  Also this will be set up on a 12v vehicle so will it require an
  invertor


What is the supply range of the motor? Depending on the required torque and response time, the 12 V may be sufficient. Invertor is not necessary.

Also care for the back EMF protection, stall detection and protection of circuitry from the huge fast voltage spikes expected from a normal vehicle battery.