Diamond-Bladed Saw
Lapidarists -- people who specialize in cutting precious and semiprecious stones -- spend in excess of $11,000 for a diamond-bladed rock saw. This is the way most professionals, including geologists, open geodes.
Pipe Cutter
For $500 or so, you can purchase a large pipe cutter. Geology departments generally have one on hand. It is a device that presses a rolling carbon blade against pipe to cut it cleanly. The same method is used on some rocks. Success with pipe cutters and geodes is not 100 percent.
The Sock Method
For geodes that are four inches in diameter or less, use the "sock method." Put the geode in a sock, lay it on a firm, flat surface and tap it sharply with the flat edge of a brick hammer. This also keeps flying bits from finding vulnerable eyes.
Hammer and Chisel
Finally, there is the old-time method of hammer and chisel. With a flat-faced chisel, tap and score circumferentially until you can clearly see your score line etched all the way around the geode. Set one side of the score line directly down against a firm surface. Place the edge of the chisel on the score line atop the geode. Hold firmly and give it one authoritative strike with the hammer, and the geode will fall in two.