Without stirring it (or maybe after first stirring very carefully, without breaking the skin), you decant most of the paint off into another container. You then scrape off the sludge from the inside of the lid, add it to the paint you have decanted, and stir it in well.
After you have used the paint, if there's still some left, you can pour it back unto the original tin until the next time you need it.
Once opened, I suspect that a re-sealed tin often allows small amounts of air to get in. Storing it upside down probably helps the lid to be absolutely air-tight - just make sure it doesn't leak!