Going from one shift register to two shift registers
It sounds like the primary issue is how you've connected the two shift registers.  You just need the bit shifting out of the first one to shift into the second one so they act, together, as one longer shift register.



The example pictured is described in full here, under the heading "Example 2":
http://arduino.cc/en/tutorial/ShiftOut

As Klaus mentioned, you want to first ShiftOut the byte you intend to wind up in the second resister, then ShiftOut the byte for the first register.  This will push your first byte through to the second register.