The black wires go to the ground terminal on the jack. There brown wires go to one side of the power switch. You supply a wire (maybe you have some left over from trimming other wires) from the other side of the power switch to the plus side of the plug. Better is to put a fuse in line with your that last wire but the type and value are debatable. I have a 3 amp fuse in there but suspect a higher amp fast blow would protect the circuit better from the "fat fingered shorts" that I tend to make versus more complicated circuit failures that I know nothing about.
Related: I use the shunt pin on the jack to switch between external power plug and an internal x8 AA battery pack. Connect the battery ground with the others on the plug. Connect the plus wire from the battery pack to the shunt pin on the jack. Done!? It's also possible to use the shunt on a second jack (not supplied) to automatically switch in addition volts from a second power source or to use the volts from the first jack if nothing is plugged into the second plug (but there will be sad faces if the two supplies are not isolated.) Speaker jacks (often) have shunts as well that can switch between? external and internal speakers. I think it's easier to figure out what the pins one the jack do when you know what they're used for.
Hope that helps!