Wait until the time of year when the lawn grows most rapidly so that it can recover from any damage caused by the aerator. For cool season grasses, such as Kentucky bluegrass, the growing season often starts in the fall. For warm season grasses, such as Bermudagrass, rapid growth starts earlier in the summer.
Water the lawn two days before aerating during dry weather, or wait until it has not rained for two days during the rainy season.
Mark underground hazards, such as pipes or sprinkler heads, with chalk or tape.
Aerate the lawn by pushing the lawn aerator across it. Aerate it in two directions to make sure no spots are missed. The aerator creates small hollow cores in the lawn, which allow water to drain through them.
Apply a layer of peat moss, compost or wood chips to the surface of the soil. These organic materials drain better than clay, so they improve the drainage of the lawn and help prevent mud. Apply 1 to 3 inches of the organic material. Keep in mind that the soil might also need an application of nitrogen along with an addition of large amounts of wood chips or bark.
Incorporate the organic material into the soil with a tiller to a depth of at least 6 inches.
Reseed the grass.
Dig a trench for a French drain in areas with a 1 to 3 percent slope and lots of water runoff. Dig a trench that is about 2 feet deep and 1 foot wide. Start the trench at a high point in the yard or a source of water in the yard, such as a gutter runoff pipe. Direct the trench down the slope, and toward an area that can stand to get muddy or that has better drainage than the rest of the yard.
Line the trench with geotextile or weed cloth.
Put 2 to 6 inches of gravel in the bottom of the trench.
Put a perforated PVC pipe along the bottom of the trench. If a gutter pipe or other source of water drains into the yard and makes it muddy, consider connecting the water source to the pipe so that it flows down the trench instead of into the lawn.
Put a t-shaped perforated pipe at the end of the trench to help disperse the water and prevent it from pooling. Connect it to the end of the perforated PVC pipe using a PVC pipe connector fitting, which many hardware and home improvement stores sell. The fitting will be a short section of slightly wider tube than the pipe. It will allow you to put the ends of each pipe into the ends of the fitting, connecting them together.
Fill the trench in with gravel.