Agates often have wavy bands of colour, bringing a sort of fire to the gem's appearance once properly cut and polished. Cutting agates requires the proper tools, a gem saw and grinder at the least. For delving into crevices, use of a flat grinder will help. In cutting an agate, you must cut according to the gem's natural features, allowing the gem to guide the cut. Don't try to force the shape. For the final polish, the simplest method is to use a rock tumbler.
Wet and inspect the rough gemstone under magnification with a bright light source. See if you can see any of the agate's "fire" or wavy layer before beginning to cut.
Shave off any outer layers over the agate. Chances are a chalcedony cap is covering your agate. Using a trim saw, carefully remove these layers. Do not cut into the dark agate stone.
Grind off the final layer, working your way carefully to the agate. Follow the stone's natural shape, letting it tell you where to cut and grind. Use the edge of the grinding wheel to follow any hill-like contours and for getting into crevices. Start by grinding along one hillside, then switch and use the opposite edge of the wheel for the opposite side of the hill. With care, the face of the wheel will do the work while the edge is barely worn.
Polish your cut agate by tumbling it in a rock tumbler. Agates tumble very well and should produce a gemstone worthy of being hung as a pendant or simply put on display.