There are several different ways to kill a lawn. One way is to simply dig it up. This can work if you are able to remove all of the roots of the old grass--many types of grass will simply be spread further if their roots are broken and left in the ground. Another way is to spray an herbicide on the lawn. One problem with most common herbicides is that they do not kill weed and grass seeds, so even after the grass lawn is killed, new weeds and grass will appear. A better approach is solarization. Start the solarizing process during the hottest months of summer.
Trim trees where necessary in order to allow as much sunlight as possible to bake your lawn for as much of the day as possible.
Set your lawnmower to 1/2 inch and mow the lawn. Some people refer to this procedure as "scalping" the lawn. The idea is to expose as much of the soil to the sun as possible.
Water your "scalped" lawn. Approximately 1/2 inch of water will be sufficient.
Cover your lawn with sheets of clear plastic. Weigh down the edges of the plastic with sandbags, pieces of wood or anything else that will prevent the wind from getting under the plastic.
Leave the plastic in place for six weeks, allowing the sun to bake the lawn under the plastic. Temperatures under the plastic should reach in excess of 130 degrees Fahrenheit and will. Over a six-week period, bake the roots and kill all of the seeds in the soil.
Remove the plastic after six weeks and rototill the lawn. Rake up as much dead vegetation, rocks and other debris as possible and level (or grade the lawn) with your rake.