According to AskMen, techniques to keep shirts from wrinkling include hanging and folding clothes immediately after they finish drying. Take shirts out of the dryer immediately when it buzzes and flatten out any wrinkles to help make the shirt look less wrinkly and reduce the need to use the iron so much.
If the shirt is either knitted or a T-shirt, it should be folded and stored in a drawer. Fold it along the natural creases of the shirts, and avoid creating large piles of shirts. The extra weight created from the shirts folded on top may exacerbate fold lines and make wrinkling more intense.
If the shirt is a casual or dress shirt, place it on a hanger that is either stretchy plastic or padded. Wire hangers can distort the shirt's appearance over time. As with the folded shirts, avoid bunching the shirts on hangers together in order to reduce the risk of wrinkles.
A costlier option to avoid wrinkles is to buy shirts made from wrinkle-free fabrics. For wrinkles that cannot be prevented entirely, lightly spray the shirt with water and dry it for no more than 15 minutes in the dryer, or take it to the dry cleaner.