Wait until the site and weather dry, to avoid working with mud or standing water. Soil amendments won't be effective with standing water or mud in the site. Dig a shallow, sloped trench from the site to a more convenient drainage route to give any remaining water a new direction, and to guide water in the future.
Find the source of the water problem. If water is draining into this site from a specific direction, build a small, temporary shield for the muddy site. Stack rocks and stones along the edge of the site to divert some of the entering water in the next rainstorm.
Amend the soil in the muddy patch for better elevation and water absorption. Turn 3 to 4 inches of kitty litter into the muddy soil, to a depth of 10 inches. Repeat with 2 to 3 inches of sand. These materials soak up water to prevent mud.
Turn 3 to 4 inches of organic compost into the amended soil. The compost soaks up moisture and raises the soil level at the site to increase drainage and discourage any standing water.