Does anyone know how to tell the Eagle PCB layout to put some components on the back of a board? I want to produce a two-sided prototype but after much googling and poking Eagle, I'm still stumped
Your question would be better suited to the Eagle community, but oh well. You want the mirror command. edit -> mirror or use the button underneath the move crosshairs.
You're putting actual components on the back side of the board? I assume this must be SMT components?
Try using Diptrace package, realatively simple yet full of features. And they have a free version on website.