No matter how careful you try to be, it seems inevitable that paper will wrinkle. While it might seem easiest to just throw it out and start again, you can be frugal and iron most wrinkles out. But if the creased paper is an old or valuable document, you would do better to take it to a professional archivist-restorer, as ironing paper does carry risks of fading or burning.
Gather the Supplies
To remove wrinkles from paper, you need an ironing board or a smooth, flat surface such as a countertop or sturdy, heat-safe table. You'll also need an iron, a spray bottle filled with distilled water and some type of absorbent material. Hand towels, pillow cases or sheets work well for this project; you can also use thin pieces of cardboard such as poster board, although fabric usually works the best. You can use paper towels; but the textured surface might imprint the paper you are ironing, and inks and dyes can be transferred as well.
Test the Paper
Spread one of the towels or other absorbent items on the ironing board, smoothing out any wrinkles or creases. Lay the paper on top and mist a small section on an edge or corner lightly with distilled water. Avoid soaking the paper. You only want it to be slightly damp. Hold the mister 10 to 12 inches from the surface to prevent over-moistening. Don't mist the entire sheet until you have tested the small section for fading or ink runs. Once you're sure the colors are water-safe, mist the rest of the sheet.
Iron the Paper
Cover the paper with a second towel or other material. Heat the iron on its lowest setting and press it, working in circles on the towel. Keep the iron moving to avoid scorching either the towel or the paper. Check under the towel to see if the wrinkles are gone. When the paper is smooth again, remove the top towel and allow the paper to finish drying, if needed.
If you aren't in a hurry to have your paper wrinkle-free, mist it lightly and place it between heavy objects such as a stack of hard-bound books. This reduces the risk of scorching or burning, but it will take several days to work. Other options include dampening the paper and stretching it on a smooth board or other surface and clamping the edges in place until the paper dries flat and wrinkle-free. If the wrinkles are small and few in number, you may be able to use the edge of your hand to press the dampened paper.