To drill through a material like flagstone you will need something called a hammer drill, which puts extra pressure on the stone and makes it easier to get through the hard surface.
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Choose a bit for the hammer drill and insert it into the hammer drill. This type of drill uses special bits. Make sure your bit is one that can be used with this type of drill.
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Place the tip of the drill bit on the stone where you will be drilling. Slightly press the trigger to start the drill in a slow motion. Bore a small hole in the stone on this slow setting.
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Increase the speed of the bit as you get farther into the stone. Press the bit into the hole and continue to bore into the stone.
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Keep pressure on the bit until it passes through the stone. Hold the drill trigger down and pull the bit out of the hole.