Determine the slope of the land so you know how much lawn grading is necessary. Ideally, you need 1 foot of drop for every 50 feet away from your foundation. Attach one end of a 50-foot length of string to a stake and place the stake in the ground near the foundation of the house. Tie the other end to a second stake and place that stake 50 feet from the house. Use a level to level the string. You may need to do this in several locations around the perimeter of your house.
Use a tape measure to determine how high the string is from the ground at the 50-foot mark. If it's 12 inches, the slope is just right. If it's less than 12 inches, you should consider adding more slope to your yard. The difference is how much soil you need to grade off the lawn. If it measures more than 12 inches, you have more than adequate slope.
Rent a skid-steer tractor with front loader to move the dirt. Remove 6 to 8 inches of topsoil from the area where you are adding more lawn drainage. Place the topsoil in a pile. Remove the subsoil and put it in a separate pile. Once you remove enough subsoil, replace the topsoil and smooth the surface slope. If you only need to adjust the slope for a small portion of your yard, you may be able to do it by hand with a shovel.
Build up low areas by removing the topsoil. Put the subsoil you removed earlier in the low spots. Cover them with topsoil.
Clean up any rocks, roots or other debris on the ground's surface. Use a rake to smooth the surface of the ground. Flip the rake over and use its back to smooth the surface even more.