long thread here.. maybe this one was already mentioned..
I made my own 6" dust collection blast gates, so I needed to cut many 6" holes (wheels as scrap.. would have been pretty close to 5-3/4")
I made a simple router jig. They sell ones with the pin holes positioned for various sizes. I made one for my exact needs. It's basically a baseplate with a hole in it such that the math works out to cut a 6" hole. So the pin radius, plus gap, plus the bit size (used the smallest plunge straight bit I had) equals the radius of the circle. I think I used a nail for my pin. I cut the pin to be the right length as it was under the router.
example jig.. you can make your own if you only have a few sizes you want to cut.
formatting link
shoud now get the idea.. basically a baseplate with a pin hole to pivot the router around. The pin hole could well in fact be under router for smaller circles.
To hold this all together -- use double stick tape. I'd suggest good quality tape. You really don't want the piece coming loose. If I recall correctly the biggest annoyance is I wanted to cut the hole in the assembly -- which was two pieces of 3/4" material and one piece of 1/4" material for a thickness of 1-3/4". I could not plunge that deep, so I had to cut down on one side, and then flip.