Assess the situation to discover the problem with the well. Your well may be too shallow, causing the water to puddle, which creates mud. Alternatively, it may actually be too deep and dirt from the edges of the well may be falling into the well, creating mud. Additionally, the type of dirt in your location may vary by depth and the mud may be being created by the dirt at the bottom of the well, or by that on the sides of the well.
Pump the well partially dry, if possible. You may want to retain the pumped water in a bucket to avoid waste. Pumping the well makes the process of reinforcing it -- and letting the dirt settle -- smoother.
Scoop out mud with your hands, a small shovel or a bucket. Avoid disturbing any additional dirt in the area.
Place 3 to 6 inches of gravel in the bottom of the well, if that seems to be the source of the mud. The gravel weighs down the dirt and keeps it from creating mud in your well.
Brick and mortar the sides and bottom of the well to prevent mud from seeping into the well. The well needs to be completely emptied of water to do so.
Cover the well to keep surface dirt from being kicked into the well by people or animals. This also gives the mud a chance to settle, making the water clean.