I started a thread on framing a flag. It was an easy process for someone like me who really isn't a woodworker. I've since done over ten and I'm still happy with the results. You'll need to search threads started by me to find it.
In your case, a couple extra steps, one would be that the back board would need to be heavier duty than eighth inch hardboard. If you don't want your sign altered in anyway, you would create a frame in the frame to hold it in place. Weight was an issue for my larger frames. I needed to attach a one by two to the wall with a 45 degree cut along the top. A similar one by two on the back of the frame so that when hanging they lock together yet can be removed easily.