A viewer sent in the tip of pouring a little water over left-over drywall compound to keep it from drying out and then just pouring it off before starting the next job. It does work, and you can get the same results by pushing a sheet of the plastic food wrap right down into contact with the surface of the compound. In both cases there are two things you should do to prepare compound for storage. First, smooth off the surface of the can, throwing out any chips that have fallen in during the day. Then wipe clean both the inside of the bucket and the lid so that there is nothing left there to dry up and fall into your nicely protected compound.
If you have ever tried to save drywall compound that comes in the box with the plastic wrapper, you have figured out that this is almost impossible to do -- there is always some compound that dries on the plastic, and that then falls into the compound when you open the plastic to get a new job started. Only buy these large boxes of compound if you are ready to use the whole box in a single day. If you can't use up that much in a day, then stick to the buckets that can be wiped clean before storage.