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Quartz crystals are silicon dioxide, SiO2. Pure quartz crystals are colorless, but impurities in the structure lead to beautiful colored gems, including amethyst, rose quartz, and citrine. Most natural quartz crystallizes from magma or precipitates from hot hydrothermal veins. Although man-made quartz is produced, the process requires heat not generally possible in a home setting. It's not a crystal most people want to try to grow at home, since glorious perfect crystals require specialized equipment.
Synthesized quartz is made using the hydrothermal process in an autoclave. You probably don't have one of those in your kitchen, but you may have a smaller equivalent -- a pressure cooker.
If you are truly determined to grow quartz crystals at home, you can grow small crystals by heating silicic acid in a pressure cooker. Silicic acid can be made by reacting quartz with water or by acidification of sodium silicate in aqueous solution. With either technique, the main problem is the silicic acid has a tendency to turn into silica gel. However, the home pressure cooker method of synthesizing quartz crystals is possible. It was done by German geologist Karl Emil von Schafhäutl in 1845, making quartz the first crystal grown by hydrothermal synthesis. Modern techniques can be used to grow large single crystals, but you shouldn't expect fabulous gems from a home canning system.
Fortunately, there are similar-looking crystals you can grow at home. One rather spectacular option is to make a fulgurite, which is the glassy shape made by a lightning strike or other electrical discharge into sand.
If you're seeking a large colorless crystal to grow, try alum crystals.
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