This is super easy to do. You will be able to smell if you did it wrong. These fermented vegetables will be a lot like sauerkraut when they are finished. They'll have a slight sour smell and a salty taste.
The most important tip I have is to use an airlock- purchased or hobbled together as you can see I did. OR, keep a lid on your veggies and unscrew once or twice a day to let out the gasses. Whatever you do, don't just put some cheesecloth on top of it or otherwise let air get in. This will make your veggies smell really nasty.
1/2 pint shredded carrots, radishes, cabbage, or other vegetable
1-3 tsp. salt
1. Shred or mash up your vegetables. So far I have only used this salt-fermentation method on carrots and radishes, but I've heard it works great for cabbages too. You may notice that a pool of juice forms on your cutting surface. SAVE THE JUJICE! Resist the urge to drain off your vegetables, as the juice is very important for preventing mold. The more juice you have, the longer your veggies will last in the fridge.
2. Stir in some salt. I use 1-3 tsp. per half-pint jar of veggies- more to be on the safe end.
3. Put the veggie-salt mixture in a glass half-pint canning jar. Compact the vegetables down until they are covered in their own liquid. Any veggies above the 'juice line' will have the ability to mold.
4. Screw on the lid/airlock and let sit for 3-4 days. When sufficiently sour (to your taste), refrigerate.
I use yummy fermented radishes as a condiment. So far I have not gotten Hubs to eat any, unless I sneak them into his stir fry. Muahahaha.