There's one thing we all have in common: breathing. When we're in tents our breath expels warm air that comes into contact with the cool sidewalls, forming little droplets of condensation. So it's water trapped inside--not water from the outside!
A few easy tricks are to increase ventilation by opening vestibules and doors when possible, or (usually in the morning) unhooking one side of the rainfly and partially pulling it off the tent to let the breeze dry things out. Just don't forget to re-secure the fly before you leave the site.