Stone spheres are used for decorative and practical purposes from water fountains to the Atlas Ball that extreme weightlifters hoist in competitions. Any type of durable stone will make a suitable sphere, but the most common are made from granite. This hard rock takes a long time to chip away, making the end result all the more valuable. While the effort involved is time-consuming, the process for carving down a stone sphere involves just hammer and chisel.
Saw off all eight corners of a stone block with a diamond tipped rotary saw blade. Place the stone block at an angle to the saw, so only a corner edge is touching the blade. Turn on the blade and press into the blade with the block. It will slowly cut through the stone, removing the corner. Wet the stone and the blade periodically. You will only be able to remove about an inch of stone with each corner, but this cuts down on some of the chiseling you'll have to do on the stone.
Mark a half-circle the size of the sphere you want on one edge of a piece of cardboard using a protractor or compass. Cut out with a pair of scissors. Set the half-circle cutout aside and keep the negative. This negative piece will serve as a template for creating the sphere.
Hold a chisel firmly against one of the edges on the stone block at a 45 degree angle. Hit it with a hammer. A small chip of stone will break off. Place the chisel further down the edge and repeat. Continue this process until all of the edges are chipped away. Try to maintain consistent hits with the hammer so as to remove roughly the same amount of stone each time you strike.
Place the cardboard template over the top of the stone. There will be gaps between the edge of the negative and the stone. Use a marker to mark straight lines along all the edges of the stone sphere that make contact with the edge of the template. These are raised areas that need to be chipped away.
Chip away all the areas you marked with the marker. Check again with the template. Mark again, going all of the way around the stone sphere. Chisel away the marked areas. Repeat the process until the entire template edge rests against the stone on all sides. The sphere won't be smooth yet.
Sand down the stone sphere to make it smooth using a disk sander with silicon carbide disk. Check the stone with the template periodically to ensure you aren't sanding down the stone too much on one side. Use progressively finer grit disks until the stone is smooth.
Polish the stone with a buffing pad and some fine polish until it is smooth and shiny.