How does a CD-ROM rotor know when to stop the moving plate?
The easiest method is limit switches.  Have a reversible drive mechanism and put limit switches at each end.  These can be wired in series with the driving power in a normally closed configuration to physically remove power at the stops.  Or the switches can be used as logic inputs to tell the micro to stop.  With a double pole switch it might be best to do both, to keep from accidentally powering the drive past the stops.

Using an RC servo might be an easy solution, with the position controlled by pulse width.  Alternatively, you can use a potentiometer attached to your drive mechanism as a servo does to get position feedback.  This would run into an ADC input or separate external ADC chip.  It would give you more feedback at to actual position, but be less accurate at the stops.

If you are unfamiliar with driving a motor both directions from a logic output, you might want to look at an H-bridge.  This allows reversible drive from logic inputs.