How do you dry up wet soil?

It depends on the amount of soil and how the soil is currently being used. If it's a small amount of soil and it's not surrounding a potted plant or other type of plant, you can spread it in a shallow pan and heat it in the oven.

If it's in a pot surrounding a plant, you could aim a hair dryer on it on low speed at a cool heat (so as not to fry the plant), in combination with slighty scraping the top of the dirt loose. If the dirt is loose, you could remove it temporarily until you've got the main part dried out somewhat. Be sure to replace the soil you removed right away.

If the wet soil is on a carpet or floor, just set up a floor fan on it to dry it out and then vacuum it up or sweep it away when done.

If it's outside in your garden--that'll be a real chore. You'll want to scrape the top of the soil loose again, being sure not to disrupt any plants. Then you'd have to set up some large fans and possibly some heat lamps for the night time. It will take a good day to get a start on drying out soil in your yard.