You can have a beautiful green lawn and then after a heavy rainstorm find that you have lots of small ponds. These low areas indicate that your soil is not only slow-draining but also that the area needs to be filled in to reduce puddling. Getting it under control so that the rainwater drains away without puddling takes some action.
Estimate the amount of topsoil you will need to fill in the low-lying area. You can accomplish this by setting in stakes on the high sides of the puddle. Run a string across so that it is flush with the ground on either end.
Now measure vertically from the string down to the lowest part of the area. This gives you the depth. Measure the length and width of the puddle. Use this formula: 3.14 (pi) x Length x Width x Depth = cubic area. This is approximately how much topsoil you will need to fill the void.
Shovel or wheelbarrow the calculated amount of topsoil into the void and level it with the back of a garden rake. This topsoil can be a mix of sand and topsoil and peat moss, depending on what type of soil you have. Mound the area just slightly--about an half an inch, since it will settle with water.
Water the area lightly and sprinkle a generous amount of grass seed over the dirt. Work it in lightly with your rake so that the first half inch of soil is scratched up with the seed. Sprinkle the surface with hay if you are worried about erosion.
Water the area every couple of days with about a half an inch of water. You want the soil to stay moist until the seed roots itself. Afterwards, water only if it is very hot and dry and there has been no rain.
Apply another half inch of topsoil if the area settles too much. This will allow the existing grass to continue growing, holding the new topsoil in place. Keep traffic off the area until it has filled in to look like the rest of the lawn, then water and mow and fertilize with the rest of the lawn.