Cut your grass with a lawnmower as close to the ground as possible to begin the sod removal process. If you have a small lawn, use a grubbing hoe to pry up the sod. If you're grading a large area, rent a sod cutter, which you pass over the lawn like a lawnmower. When you've removed all the sod, pull any weeds that linger in the area.
Scrape any high areas of dirt away with a heavy rake or shovel until your lawn area is smooth.
Add as much topsoil as necessary to your lawn to raise it to the desired height, then cultivate the lawn area 4 to 6 inches deep to thoroughly mix the old dirt and the new topsoil. If you don't combine the two elements, you can run into drainage problems in the future. It's natural for the surface to sink once it's cultivated. When this happens, just add more topsoil to raise the lawn surface to the desired elevation.
Rake the soil into position using a wide landscaping rake. The ground should slope away from your house, dropping by a rate of between 2 and 3 inches for every 10 feet.
Water the entire area heavily until there's enough water to pool in areas. The areas in which the water pools will show you the low areas that you'll need to fill with topsoil. Continue this process as many times as is necessary. Eventually, you should have no pooled areas and the water should gradually but steadily trickle away from your house. When the entire grade is smooth, you can plant your new lawn.