Wait until fall to kill bad grass if you want to use an herbicide containing glyphosate. Spray the entire area of bad grass with the herbicide and wait a few weeks. Once the herbicide penetrates the roots of the grass, the grass dies. If you want a natural alternative to herbicide, use white vinegar in a spray bottle to get the same effect.
Go over the entire area of bad grass with a tiller if you do not want to wait until fall to kill the grass. Break up the soil 6 to 8 inches deep and then even out the tilled soil with a shovel so that the ground sits as flat and even as possible.
Lay 10 to 12 layers of newspaper over the surface. Use a garden hose to wet the newspaper until it is wet through all of the layers.
Place black plastic, such as trash bags or black landscape fabric, over the newspaper. Use rocks, bricks or cement blocks every few feet around the perimeter of the plastic or landscape fabric to hold it in place.
Mulch at the base of all trees, shrubs and new plants in your yard where bad grass grows. Mulch kills the grass at the base of the plants and prevents its regrowth.