Put the sliced red onions and sugar into a mason jar, packing them in tightly.
Pour the salt water brine over the onions leaving a half inch to inch of headspace at the top.
Add your fermenting weight over the onions in the brine to be sure the onions stay submerged. If you do not have a weight, just be sure the onions are completely submerged in the brine or you will get molding.
Put your fermenting lid on the jar (I use pickle pipes) and leave in a warm space in your kitchen on the counter or in a cupboard for 1-3 weeks. You can taste the onions along the way to get your preference of tartness. If your house is warmer, it will ferment faster, and if your house is cooler, it will take longer. Everyone has a different taste for fermented foods. Your fermented onions should smell oniony and taste pleasantly tangy/sour. The longer you ferment the more beneficial bacteria will be present. I ferment my onions around 3-4 weeks if it is winter time and cooler in my house, and it takes more like 2 weeks in the very warm summer months.