Prepare the Solution
All you need to do to prepare the crystal solution is to mix as much potassium alum as will dissolve into 1 cup of very hot water. You can add food coloring to tint the crystals. The natural color of the crystals would be clear or white.
I poured the solution into a clean bowl, trying to avoid getting any undissolved material into the new container. Allow the crystals to grow overnight. If your solution is very darkly colored, you won't be able to see whether or not you have crystal growth. You can use a spoon or fork to scrape crystals from the bottom. To get a large single crystal like this one, remove all of the crystals and return a few that have the desired form to the solution so they can continue growing. Remove them and allow them to dry when you are satisfied with their appearance.
One common form taken by this crystal is a regular octahedron with flattened corners. The colored crystal resembles a ruby. In fact, the first synthetic ruby was produced by Gaudin in 1837 by fusing potassium alum with a little chromium (for color) at a high temperature. A synthetic or natural ruby has a Mohs hardness of 9, while a potassium alum crystal only has a hardness of 2 and is readily soluble in water. Therefore, while your overnight-crystals may resemble a ruby, they are too soft and fragile for any purpose besides display. Even though they aren't real rubies, these crystals are well worth your time since they are so so easy and quick to grow and have such a beautiful form.