Cold stabilization is done by just exposing the wine to temperatures as close to freezing as possible (32F - 0C) for a minimum of two weeks (longer will not hurt the wine, it just will slow down the ageing process). A minimum of 40 F for two weeks is necessary for successful stabilization.
When you cold crash your wine before packaging, you cause tartaric crystals to precipitate out of the wine. They will be left behind in your carboy instead of settling out in the bottle. If you do see crystals in your bottle, they are only a cosmetic defect and won't hurt you to drink the wine.