I'm completely new to lighting - please bear with me.

Can someone look at the attached image and tell me if I've hooked these suckers up correctly? I'm referring to the connections rather than the control settings. The controller is an Elation Stage Setter-8 with two (2) Elation DP-415's

Yes it is correct, you might want to consider only running one of the DMX lines out of the console, and into the first DP-415, and then running DMX out of the first DP-415 and into the second. 9 times out of 10 it is easier to daisy chain DMX rather then running 2 separate lines (of course it depends on the setup).

Thanks for the quick response - after your post I'm confident I won't fry either the system or myself