This, of course, is why the bridges come off so rapidly on newer guitars. Do you see how only a center portion of the bridge was actually glued to the top? The outside 1/8" of its footprint wasn't even glued as the factories spray their tops before fitting bridges. This is common to most every modern factory-built guitar these days and even applies to this one -- a quite high-end, 10-year-old Martin.
The downside of this practice is obvious -- you're losing a major amount of gluing surface. It's effectively turning the improved footing of a "belly bridge" into the smaller footing of the old "rectangle bridge."
The first part is to prep the surface. I mark the bridge's area with a pencil and then use an angled chisel or x-acto knife to slice through the finish. I chip the finish off and then use sandpaper to get down to wood.
After that I take the bridge over to my belt sander to remove any glue remnants and use my trusty StewMac bridge regluing jig to clamp it all down to the top. I have a bit of hardwood I use under the bridge plate to apply clamping pressure to.
Unfortunately the aluminum bridge gluing jig is excellent except for when you're dealing with a top that's lightly domed or distorted and the extra "back" of a belly bridge. For that I use smaller clamps and a block of wood to apply pressure directly to the rear of the "belly" and snug it to the top. If the block wants to slip I c-clamp it to the gluing jig just to hold it in place. This c-clamp is way overboard but I'd used-up all my smaller clamps on other projects at the moment!