Hi,
you can made different construction. The traditional conveir belt is a one or two draving wheels, depend from this one or two direction is movement, and several secondary wheels between them. The belt can be set in motion with friction or with cogwheel.
In your case i think you can use cogwheel construction, from old donuts cooking machine, they use a cogwheel and mortiser belt. You can also made a simple construction with two pulley and wire. To drive the DC motor in only one directin you will need relay or transistor. To detect the position yu can use the optobarier sensors.