It seems that the information that you will need in order to read the output from the reader is contained in one or more of these documents (from the data sheet linked in reply #8).
SHIFT-OUT TIMING
Refer to MagTek specification 99875337 (99875336 or 99875259 for 5V units) for details of the Shift-
Out Timing.
The shiftIn() function may be of interest for reading the data.