Clean the top surface of the tiles if you are able to do so using a damp cloth and some cleaning solution. Cut a piece of contact paper so that it is bigger than the mosaic tile design surface. You may need to attach two pieces of contact paper together by revealing some of the adhesive side. Remove the protective paper and firmly rub the adhesive side to the mosaic tile pattern.
Cover the tiled surface with a wood board and hammer the board to break loose any tile pieces that are still grouted to the surface. Move the board around and repeat the process as needed.
Turn the surface over quickly and carefully, trying to keep intact the design pattern by having it stick to the contact paper. Use pliers and brushes to remove any grout or cement that came along with the tile onto the contact paper. If tile pieces remain on the original surface, use the board and hammer to remove these and place them as best you can where they belong in the pattern.
Remove all cement and grout from the original surface using water, steel wool and sandpaper. You may have to experiment to see which combination of these materials works best for your project.
Air-dry the original surface completely and prepare the thin-set cement or grout. Apply the cement or grout using a small notched trowel.
Re-attach the mosaic tile pattern to the newly grouted or cemented surface. You can do this in two different ways, depending on your preference and the size of your project. You can lift the contact paper and quickly flip it over onto the surface or you can flip the surface over and place it on the backs of the mosaic tile pattern. Press the tiles firmly so they are evenly and securely attached to the table. Let the cement or grout dry overnight.
Pull off the contact paper and use fine-grain sandpaper to sand away any grout or cement bubbles. You may need to use a flat trowel to apply more grout or cement between the tile pieces. Let this dry for 15 minutes and then wipe the surface with a damp sponge to remove material on top of the tiles.