When using the high powered shift registers, use the code and generally follow the tutorial for the low powered ones. However, the pins are labeled differently. Here's how to wire it up:
Unlike the low powered shift register, this one expects to use the 8 LED pins as sinks (i.e., drains), not as sources. That means you need to wire the LEDs differently. Positive voltage should come from VCC through the LED and resistor, and drain at the shift register.
A detailed wiring diagram can be found at the bottom of this blog entry on using these shift registers.
If you connect more than one shift register together, repeat the above. On the second shift register, connect its Pin 3 (data) to Pin 18 of the first shift register. (The datasheet for this high powered shift register labels Pin 3 as "SER IN", and Pin 18 as "Ser Out".)