Learning Gates (AND, OR, NOT, NAND, NOR, ect) and just can't seem to grasp circuit diagrams
I don't usually answer homework this completely, but as you seem at a loss as to where to start:

Consider a simpler starting point.

If I have a number of 2 input OR gates and wish to make a 3 input gate, then assuming input names of A, B and C, then connecting the A and B inputs to gate 1, connecting the output of this gate to gate 2 and putting input C on the other input of gate 2 achieves a 3 input gate.

Taking your NOR gate:


A very important point to note is that the OR term is available. To make a 3 input NOR then we will take 2 2-input OR gates and do a final inversion for NOR.

So here then, we have:



If the images are not that clear, the OR output for your 2 input gate is just before the final inversion; use two of these and then add the final inversion.

The inversion term can be confusing at first, but the key here is to understand that the non-inverted term is available; cascading the non-inverted terms and then adding the final output inversion achieves the requirement.

HTH