RazorFly:
(I figured I should connect the data in to Q7 on the previous register)
That's right.
but where does clock go?
The same clock signal goes to the clock input on each IC.
what does the bit string look like?
You don't say what method you're using to interface the shift registers. I'll presume that you're using the shiftOut() function. The output value for that function has the type byte, so it's eight bits long. If you want to shift three bytes, you'll have to call the function three times.