That device has "sink" outputs that switch to 0V / negative.
That means you need a common-anode type display, and link each cathode pin to one of the outputs of the TPIC6C596 via a suitable resistor to set the segment current, and connect the display anode pin to positive power.
Software wise, you need to create a "look-up table" or array, with a list of the bits that need to be "on" for each 7 segment pattern, and matching the display wiring you use.
eg. If segment A is bit 0, B is bit one etc. in sequence, this should be suitable:
To transfer to the shift reg / display, look up the display digit in the table and store it in a memory location or register; I'll call that "pattern".
If you want the decimal point on, set bit 7 of the pattern or OR with 0x80 (same effect).
Copy bit 7 of the pattern byte to the pin you are using for data out to the shift reg, then set the clock output pin high and then low to store that bit.
Shift the looked-up pattern left one bit and repeat the above, through all eight bits.
Then pulse the pin feeding RCLK high and low, to transfer the stored pattern to the outputs.
The G and CLR pins should both the high in normal use.
(ps. Please create a new thread when you have a new question - one of the moderators may move this post to a new thread for you).