I guess you need to work on your google-fu a little. My first google search of "arduino shift 7 segment" gave me lots of hits. I do notice that most of the tutorials are for 74HC595 and you have a 74HC165. A quick trip to octopart.com to look up datasheets and I see that you have the wrong type of shift register for this application. Yours is a parallel in serial out, meaning you give it 8 different logic levels on 8 pins and then read it from the chip as 1 byte, typically on 3 pins (latch, clock, data). What you want is a serial in parallel out (so you feed it 1 byte of data using 3 pins and then it outputs 8 logic levels on 8 pins) like the 74HC595.
Don't throw out that 74HC165. It could be useful on another project where you need to poll more inputs than you have pins on the Arduino.