Summarize:

You need a plastic or glass container that’s completely airtight to lock in moisture and prevent any brine from evaporating. If the original container is tight enough, leave the cheese in it. However, if it doesn’t reseal well after opening it, move the cheese to a container that can be closed completely.  If you move it to a new container, be sure to label the container with a permanent marker or sticker. Write down the type of cheese and the date that you bought it so you know how long to keep it. When transferring your cheese, keep any original liquid, too. Don’t drain the cheese. The drawers in your refrigerator have the most consistent temperature and humidity so the cheese won’t get too cold or too dry. The best drawer is the one closest to the bottom of the fridge. Ideally, your refrigerator temperature should be set between 35 and 45 °F (2 and 7 °C) for cheese-keeping.  If you’re having trouble using up your cheese before it goes bad, consider buying cheese in smaller quantities. Throw away cheese if there is any mold or if it smells funky. Mold on soft cheese is a sign it’s not safe to eat. Contrary to popular belief, you don’t need to replace the brine if you only use a clean utensil to reach in and remove cheese. But as soon as you dip a dirty utensil or your fingers into the brine, you’ll want to change it out. Drain the old brine with a cheesecloth or strainer over the sink. Then, fill the container with new brine and seal it tightly before placing back in the fridge.  Make your own brine by dissolving 1 tablespoon (15 ml) of salt in 3 cups (710 ml) of water.  Stronger brine will preserve the cheese for longer. But keep in mind that the more salt you put in the brine, the saltier the cheese will taste. Don’t swap fresh water for brine. Water will dilute the flavor of the cheese and cause it to spoil faster.
Transfer your soft cheese to a tightly sealed container if necessary. Keep the cheese in a fridge drawer for no more than 2 weeks. Replace the brine only if it gets contaminated with a dirty spoon or hand.