Use a boxcutter to repeatedly score around the sides and top of the outside trim, in order to gain access to the heater cores. This is glued in place, but around the bottom it is a small amount of glue, so if you completely separate the top and sides you can break the glue at the bottom. The air slot core with heaters will slide out.

Be very careful here. Use the thinnest blade possible and repeatedly score rather than doing it forcefully. This is hard to without damaging it.

Once you remove the silver face plate, the black and white part you see simply lifts out from the back white shell.