The goal of any fermentation is to allow bacteria to run free – but you need to make sure it's the bacteria that you introduce that is multiplying (see How to Make Whey). So make sure to clean all jars and utensils thoroughly with soap and water. Here's what you will need:
Glass Vessel: Best to stay away from plastic and use ceramic or glass. Mason jars are perfect, but feel free to reuse any well-washed jar. Be sure to rinse away all soap residues – a final wipe with a vinegar-soaked cloth is recommended.
The Lid: Cover the jar loosely with the lid. The fermentation process creates carbon dioxide that will build up and can pop the top off. It's a good idea to 'burp' the jar every day to avoid an explosion.
Weights: You don't want the fermenting veggies to come out of the fermenting liquid and touch the air (which is crowded with wild yeast and bacteria you don't want), so they need to be weighted down. You can go out and buy pickling weights, but a clean rock or stone should suffice. You can also keep a cabbage leaf or extra veggies cut and placed horizontally in the jar over the ones you're fermenting.
Salt: You want to use as natural a salt as possible with no additives – so no iodized table salt and nothing with anti-caking agents. Sea salt, pink Himalayan salt, and most kosher salts will do.
Water: Chlorine can kill living organisms, so you want to use filtered or spring water. If your tap water is heavily chlorinated and you can't filter it, fill a bowl or a vessel that allows as much surface area as possible and leave out overnight; the chlorine will evaporate. If you don't have the time for that, boil water and cool it to room temperature before starting your project.