Mine had a couple of small pieces of adhesive around the edges, and then there are two posts that fit into body holes. Once you loosen the adhesive, pull the badge straight away from the body carefully. It'll take a bit of work, but the posts just pop right out of the holes.
Have you ripped off the side moldings yet????
I haven't decided on the moldings yet. I just did my front badge on Saturday, so it's black now. I'm going to re-do it since I think it looks like shit, but no one else can really tell. I just sanded it some and hit it with some primer and some Krylon black. Let it sit a day, and then ran it through the auto wash @ Holiday to see how I did. Looks like it held, so I'll do that for the back one. The Mazdaspeed logo is going to get a bleach bath, but that's because it's simply be too hard to sand something that intricate to get primer on it.
Oh and i'm an idiot and bought white primer for a black paint job.
EDIT: And i'll maybe clear them all and bake them in the oven for that really nice finish. I'll do it when Taya isn't going to be home though. She's going to be mad enough at me for ruining a cookie sheet in the process, don't need her coming home to the place smelling like paint.