If you don’t have an iron (or don’t want to iron), this is probably the quickest method to try for de-wrinkling a shirt you need to wear ASAP.
Basically, you just hang the wrinkly shirt in question under an upward facing fan. Use a spray bottle to spritz water all over the shirt, clip the shirt to the fan, and let the fan fun for 10 minutes or so. You should end up with a wrinkle-free shirt! Check it out: