To drill holes in gemstones, you must have the proper tools and attentiveness. The most important aspects are to keep the stone situated in a stable position while drilling, and to keep the gemstone surface lubricated so as not to break the bit. A diamond bit is needed for most stones, except softer gems such as amber. Use silly putty or poster putty to keep the stone from moving around while drilling.
Fit the drill press with a diamond-tipped bit. Choose a drill bit size based on your desired bead hole size. However, there should be at least a 1/4 inch of gem all around the hole to ensure strength and durability of the bead.
Stick a wad of putty on the inside bottom of the plastic container so that the putty is centred. Stick the stone to be drilled onto the putty. Make sure enough putty is underneath the stone to allow the drill to go completely through the stone without damaging the container.
Fill the container with water, completely submerging the stone.
Keep the power off as you lower the drill into the water next to the stone. When the bit has reached a depth between the stone and the bottom of the container, fix the drill depth with the drill depth screw.
Lower the bit into the stone gently and slowly. After entering the stone 1/16 of an inch, raise the bit to allow water to enter the hole. Continue drilling 1/8 inch at a time until you reach the delimited depth.
If you're serious about drilling beads and are willing to make the investment, purchase an automatic gemstone drill made specifically for this purpose.
Always wear protective eyewear when working with power tools.