The belt pulley is installed on the pair of shaft mounts, pair of bearings and 3" screw as a shaft (1/4" dia), secured by the nut/spring lock washer/nut combination. The first nut doesn't need to be tightened too much, just to the point where there is no axial slack. Tightening of the second nut against the first will then create some slack so that the shaft will rotate easily even if shaft mounts are not in perfect alignment.
In most cases, positioning the shaft mounts manually will be good enough. If you need to make sure that the pulley shaft is at the right angle to the rail, you can adjust the position of the shaft mounts using 1/4" threaded rod as a guide. Secure it with nuts on the shaft mounts (with the bearings on) and a third shaft mount in between the two, then find the position where the threaded rod is at the right angle to the rail and tighten the shaft mounts.
The simplest support for the shaft mounts is a 4" angle attached to the rail with 1" and 2" angles.
The side for the motor would use the same arrangement except it would be 6" with 1" angle at the end instead of 4".
In the video the motor side is different - it is optimized for easy adding of the parallel rail/belt.