Where is the moisture coming from?
The first thing you need to know is that you probably do not need to worry about your water softener. The water you see on the exterior is coming from the air. Most water softeners are kept in places like the garage or basement. When warm, moist air comes in contact with the cool tank, the moisture in the air condenses to form this layer of water on the exterior of the tank.
If you think about it, this is an effect you have probably witnessed several times. When you bring a cold drink outside on a hot day, you see moisture condense on the outside of the glass. This is the same thing that is happening when you notice your water softener sweating. The amount of water that you will see on the exterior of the water softener all comes down to the amount of moisture in the air and the difference in temperature between the tank and the temperature in the room.
While a small amount of water building up and possibly dripping from a water softener is normal under the right conditions, you should take notice if it seems to be producing a considerable amount of water. If it seems to be producing a few gallons a day, it might be a sign of a leak.
What can you do?
Just to make sure that absolutely nothing is wrong you may want to call us to come out and check out your water softener to be safe. As a temporary solution, you can just put a container of some sort under the water softener. Just make sure to empty it regularly and put a small amount of bleach in the container to prevent any issues with mold.
If you want to stop the condensation all together, you could consider buying a jacket for your water softener. A water softener jacket is just a tight layer of insulation that puts a barrier between the cold tank and the warm air in the surrounding room. You can buy them at hardware stores and plumbing supply stores, you could also call your plumber to install one on your water softener.