Place a layer of paper towels on a blotter board or heavy pasteboard piece and lay the watercolor paper with the painting, if any, facing down on top of this.
Spray or blot the back of the watercolor paper thoroughly with a spray bottle or sponge; use as much water as it takes to make the paper relax and start to feel more like heavy, stiff cloth than paper. Avoid wetting down the very edges of the paper unless there is a crease in that area. Smooth the paper down as flat as possible with your hands, taking extra care around deep bends or creases.
Lay a second layer of paper towels on top of the watercolor paper and cover with a second pasteboard/blotter board.
Distribute books or weights evenly on top of the pasteboard/blotter board sandwich. Use as much weight as you can find, as this is what presses the paper fibers back into shape.
Allow the watercolor paper to dry in this primitive paper press for at least 24 hours, changing the paper towel layers and possibly the blotter boards after 12 hours. Final drying time will depend on the amount of water you used in the first part of the process, but should take around 24 hours.