You'll need scissors, an empty picture frame with removable glass pane, and glass cleaner. The first step is to remove the glass from the frame and clean both sides thoroughly, using something fairly lint-free. Hang onto your cloth or whatever for the next step. I used alcohol, because it just happened to be there. You want something that will get all the smudges and fingerprints off, so that the contact paper can stick easily and you have a nice, clean, smudge-free end product.
Next, find the piece of the contact paper you want to save. I think this would work best with a lot of negative space, so more of the paper can adhere to the glass. Using your rag to hold the glass so you don't smudge it again, carefully place your glass over your image. It's also a good time to push it into place, burnishing it and pressing with the cloth so the contact paper sticks. This makes cutting it out a great deal easier.
Cut out carefully. Try to pay attention to the edge of the glass so you don't accidentally detach your contact paper too much.
Once it's free of the larger sheet, trim as necessary and press down any edges that may have lifted. It doesn't have to be super neat unless you choose not to frame it. These would be pretty cool as floating prints too!
Now reassemble your frame and you're done! I don't know how long the chalk powder will cling, but I guess we'll find out! I bet this will work with any flattish contact paper collage. Enjoy!