There are a number of herbicides that will kill turf grass. Most are not recommended by horticulture experts, as they leave a residual in the soil.
The fastest way to remove a lawn is to physically remove the sod by cutting it into strips with a sod cutter. Sod cutters can be rented, or you can hire someone to do the work.
Sheet mulching is the most natural and beneficial method to remove a lawn. This method maintains the soil structure, adds organic matter, requires a moderate amount of labor, and does not require removal and disposal of turf.
Lawns can be killed using large sheets of clear plastic. This method works best in areas with full sun for most of the day and should be done during the warm months of the year.