Some paper crafts require folding and then cutting in shapes. The problem is that the unwanted folds remain visible. Assuming that the paper can be opened fully, what should be done to remove the fold marks on the paper?
You can iron it with not very hot iron (not to burn the paper). Another trick is to put it under some heavy books for several days.
If you are looking for a faster but not as effective way to smooth out paper, you can run the paper over the edge of a desk. (Pretend like the paper is a string and the edge of the desk is a pulley wheel) The rollers in printers also use the this principle.
If it's an A4 size paper, it's very easy to remove the wrinkles. Keep the paper on a printer's tray. Open MS Word and make a printout (ensure the MS Word file is blank). That makes the wrinkled paper to go through the printer and all its wrinkles will go away.
The paper fibres are broken. The damage is one-way. There's no going back once the damage is done.
But while you can't remove folds or wrinkles from a sheet of paper, you can leave wrinkles and folds behind.
Make a pattern by folding, wrinkling, cutting, etc. Then, use that original as a pattern to trace onto flat, unwrinkled, and clean unfolded paper for the final finished product.