These are really tricky to make, but the outcome is worth it!
Paint a wooden frame black (or the color of your choice). After it dries, sand it a lightly with sandpaper.
The background (and the back):
Cut a piece of cardboard to fit the size of the frame. Glue a piece of burlap to the cardboard (using a hot glue gun), then glue both to the back of the frame. Cut a piece of twine to use as the hanger. Tie knots on both ends, then use a staple gun (or strong tape) to secure it to the back.
Print out on colored paper whatever state or country you want to use. Then, cut out the image (use an exacto knife for tricky details). For the details around the edges, use a paper towel and inkpad to lightly dab on some black.
To get the 3D effect, instead of gluing the picture to the inside of the frame, use foam stickers to raise it up (if you don't have foam stickers, you can cut small pieces of cardboard glued together)