Soil that doesn't drain well is one of the primary causes of waterlogging. This type of soil -- usually a clay soil that's too thick to drain efficiently -- causes water to pool on the surface. You can improve soil drainage by installing a drainage system. One option is digging ditches 3 feet deep around the sides of your lawn, with sloping edges that allow water to drain instead of pooling. If your drainage has a severe problem and you don't want to uproot your lawn, you can have a contractor install drainage pipes instead.
The key to preventing your lawn from suffocating in water is making sure it gets plenty of air -- this is a smart alternative to installing drainage, too. Wait until your lawn is free of excess water before aerating to allow airflow to the grass roots. Tools you can use include lawn aerator shoes with spikes on the bottom, push spike aerators that you push like a lawn mower across your grass and mechanical hollow tiners. The holes should be at least 1 inch deep. To keep your lawn well-aerated, spike it in the fall every two to three years.
Sand is fast-draining, so it can amend clay soil that doesn't drain well. Use a push spike aerator or hollow tiner that leaves holes in the soil 4 to 6 inches deep, then fill the holes with horticultural sand. This is an easy way to improve soil drainage and aeration at the same time, without having to dig up your lawn, change the soil completely and replace the grass with fresh turf.
As a last resort, you may have to replace your lawn. Before laying down new grass, work sand into the soil to improve long-term drainage. Another option is incorporating 2 to 4 inches of compost at least 6 inches deep into the soil. You can include manure and peat moss in this compost, because they're fast-draining materials that also enrich the soil with nutrients. The new soil, along with healthy watering practices, can prevent your lawn from becoming waterlogged in the future.