Drill a hole large enough for the round bit in the middle to a depth just over the total depth of the ringpull (use a forstner or spade bit). Cut in any other mortices you may need to fit the mechanism on the underside with a chisel.
Now you can lay the ringpull down into the mortices so that the brass plate lies flush with the lid. I like to drill a couple of the holes in opposite corners at this point and gently screw it down so that it's nice and secure. Now cut around the edge of the plate with a Stanley knife, remove the ringpull and chisel it out to the depth of the plate. If you like, you could use a router for this bit to get the depth just spot on - freehand close to the the edges, then finish off with a chisel.
If you need to drill a countersink for your pilot holes - do that now, and Voila! It'll fit like a glove.
With brass stuff like this, don't be tempted to invert it and score around the edge first. It is very rarely symmetrical and so when you turn it the right way around it won't be a perfect fit.
Hmm, good question... I've never done it, it may not be the easiest way, and I'm more than willingly to learn different, but how I'd do it would be to make a recess for the middle (and I assume deepest?) bit first. That'd get the plate flush with the surface, so marking round that in order to remove the required depth should then be a piece of cake, relatively speaking. Personally I'd use a forstner bit (probably) and then a router plane, but only 'cos I don't trust myself with a powered router for that sort of task. But I might revise that if I had the actual hardware in my hand (yardarm clearing!). I wonder, am I even close? :?
In case you didn't pick up on all those caveats; I don't know what I'm talking about and I defer to anyone who's actually ever fitted one. :wink:
Rather than starting yet another thread, does anyone know how big the entrance holes should be in a dove cote, reason I ask is I'm designing and building one for a friend but having never built one before I'm a little unsure about the correct size for Doves ?