Once washed, remove the gloves, place them on a terry towel and press them lightly to remove excess water (the gloves must remain wet, not soaked). Once this is done, take the gloves and pull them lengthwise, i. e. fingers and wrist of the gloves, then take another dry towel and wrap the gloves in it without wrinkling them. Now you just have to wait for the gloves to dry, it will take some time depending on the thickness of the lining even a couple of days, when the gloves are still slightly damp wear them to make them resume the shape of your hand.(this procedure should also be used when the gloves are very wetbut maybe because you ended up in a storm)
WARNING NEVER DRY THE GLOVES IN THE SUN OR NEAR A HEAT SOURCE, they would certainly dry sooner but the skin would dry irretrievably.
It took a few words but the process as you can see is really simple and does not present any risk to the gloves, so you can think of doing it even during the season when you normally use the gloves, without having to wait until they are too dirty because at that point it would be more difficult to clean them, and the accumulated dirt could ruin your gloves.