How would I wire it with a shift register and which should I use?
Here's a shift register from Sparkfun... costs about $1.50
Read the datasheet on it and it will explain how to use it.
Basically, you connect it to the serial connection on your board, and then supply it with power and ground. Each time you send a byte on the serial connection, it shifts it into the register (1 byte = 8 bits). Until you send it another byte, those 8 bits will remain set. So, you just send a byte representing the digital outputs you want to turn on/off.
Hex Binary
0xFF = 11111111 This turns all 8 outputs of the shift register on.
0x00 = 00000000 This turns all 8 outputs of the shift register off.
0xAA = 10101010 This turns every-other output on.
So, now, all you have to do is connect each of the 8 shift register outputs to one of the segments on your display. (Remember to connect the display to ground as well.)