Made in varying thicknesses and surface finishes, watercolour paper is an important tool in the watercolourists' supply closet. Modern watercolour papers are actually made of linen or cotton and specially treated to enable them to hold the water-soluble pigments on the surface instead of letting them sink into the fabric. Despite this treatment, they will wrinkle if they get wet through the painting process or by accident. Never fear. They can be smoothed out without damage to the images on their surfaces.
Place a layer of paper towels on a blotter board or heavy pasteboard piece and lay the watercolour paper with the painting (if any) facing down on top of this.
Spray or blot the back of the watercolour 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 watercolour 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 fibres back into shape.
Allow the watercolour 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.
Leave your paper in the press until it is completely dry, changing the towels as often as necessary past the 24-hour mark. If the wrinkles and bends in the paper are very severe, the process may be repeated if the paper is allowed to completely dry and recover between attempts.
Some websites may advocate the use of irons and damp towels to smooth papers, but this may cause burns or changes in the colours of the painting.