How do you fix a toilet that sweats due to condensation?

You can buy a tray that fastens underneath the tank - very easy to install. Do a search for Toilet Drip Tray and you will see what I'm talking about.

The condensation is caused by the cold water which runs into the tank when it's flushed. Mostly a wintertime problem. The surface of the tank gets chilled. I think I have seen toilets with insulated tanks. If you're not up for replacing the toilet, the cheap fix is to wrap the tank with some sort of fabric for insulation. You can usually get these in a set with a matching cover for the lid. The other, slightly more involved, solution is to pipe hot water to the toilet with a mixing valve you can use to warm up the cold water a bit.

I have found that tanks continue to sweat when covered in fabric, and have not heard of using a mixing valve, and would be concerned that, if it failed, it could allow hot water to the toilet, which could crack the ceramic, or melt the wax seal under the bowl. At any rate, most sweating is due to high volumes of cold water going through the tank, which may be because the ballcock (fill valve) or flush valve do not seat off properly, allowing water to trickle through when toilet is not being used. Also, there may be a leak in the vicinity that evaporates and causes high humidity in the area, therefore more condensation. Running a bathroom exhaust fan more may help.