A couple of ways to do this. For a DSLR, the most practical way to stabilize is a monopod. Smoother shots when following a moving person, as well as quick displacement when needing to move yourself. As for protection of the camera, the monopod is useful as well. A box will be needed (about the size of a paint case). the open top side will be your access point. Cut a hole in the bottom (formerly the side) of the box just large enough to put the monopod through. Secure the box to the monopod with ducktape, zipties, etc. Make another hole for the lens and then the DSLR should then be secured to the mount on the monopod, obviously facing the hole. Keep in mind the type of lens you use.
Another, bit more pricy, is creating a frame from PVC pipes and cardboard. I'd refer to a youtube video for that. Its a mix between making frames, and then improvising as you go along. But remember that you'll need to incorporate the tripod or monopod in the design.