Potassium Alum Crystals
Typically, you will want to make sure that your solution is saturated. Don’t add a specific, certain amount; rather, add the solid to hot distilled water until it actually won’t dissolve any more. Then quickly filtrate the hot solution through a hot funnel (don’t burn yourself though, please). Let this filtered solution cool down and you should obtain acceptable seeding crystals in your beaker.

By using this supersaturation technique, you can be sure that


you have a saturated solution so crystallisation can occur immediately and
since you cool down the solution rather quickly and since solubility of aluminium potassium sulphate increases with increasing temperature, it becomes very supersaturated very quickly.


Once you have a seeding crystal, e.g. by this method, you can use the hanging technique mentioned by Carlos with the remaining solution (which is still supersaturated). If you do so, you can use an almost infinitely thin string; a human hair typically works perfectly and is even less visible. Another option is to filtrate the solution again so that the bottom of the flask is clean and place your crystals there to grow. You will need to turn them around every now and again to allow for even growth.

And you can make your aluminium potassium sulphate crystals even nicer by cocrystallising it with chromium potassium sulphate. They crystallise in exactly the same structure but the chromium(III) ion is coloured (aluminium(III) is not).