Design the seal on a sheet of paper. You can use historical seals, like the ones in Weizu Sun's "Chinese Seals: Carving Authority and Creating History." You can also design your own seal. You can find many sources on the Internet, such as Mandarin Today.
Design the dragon that will make the soapstone seal's handle. Weizu Sun's book is a good starting point. Draw a front and side view of the dragon on a 1 to 1 scale.
Transfer your designs to the soapstone block with a pencil. Be careful to press lightly. Even your pencil can carve the stone.
Put on your safety goggles. Carve the seal into the stone's bottom with a pointed stone-carving knife. Begin by gently scratching the characters into the stone. Using several passes, carve deeper into the stone. Wipe off the the dust with a soft cloth after each pass. Cover the seal with masking tape.
Cut the dragon's rough outline into the stone with the mini hacksaw. Round off any hard edges with your rasps. Shape the dragon with the rasps until you are ready to detail the figurine. Wipe off the stone dust.
Carve the details, scales, eyes and whiskers with your stone-carving knives. Wipe away the stone dust as you work.
Remove the masking tape. Gently sand the figurine and seal, making sure you don't erase any of your detail work. Wipe away the stone dust. Polish the project with the soft cloth until it is smooth and shiny. Protect the finished work with two coats of clear lacquer.