Lawns retain mud when the soil underneath cannot absorb water. While even the most well-draining lawn can turn muddy if storms are heavy, chronically muddy grass needs a serious overhaul. Uneven terrain can exacerbate drainage problems, since water pools in depressions. Fixing the underlying drainage problem takes a few hours, and reseeding your lawn takes several weeks for the new grass to grow.
Wait until the soil dries out, since you can't troubleshoot a muddy yard while it's still wet. When the soil is firm enough to be worked, it's time to fix your lawn.
Divert drainpipes away from your yard, since they may be adding to the mud factor. Dig a drainage ditch underneath the downspouts that allows rainwater to collect without spilling into your yard. Alternatively, set a rain barrel beneath a downspout to collect rainwater that can be used to water your plants.
Till the lawn with a rototiller. Work the rototiller over the area that gets muddy. This turns and aerates the soil. If your muddy area is in a depression, level it by adding bagged topsoil.
Broadcast up to 6 inches of compost or manure over the area you tilled, then till a second time. Organic material helps lighten the soil so it can absorb water without turning muddy. Improved soil drainage means you won't get muddy grass.
Spread grass seed over the tilled area, then moisten the area. Keep the area moist until the grass germinates.
Plant water-loving plants in your newly dug drainage ditch to have a rain garden.