Tear up your existing driveway, or mark with spray paint the area where you're installing the grass driveway. Depending on the size of your old driveway, you can either tear it up with a jackhammer and clear it by hand or hire a contractor with heavy equipment such as an excavator.
Dig a hole 6 inches deep for the driveway. Renting an excavator or hiring a contractor to do this will be much easier than digging by hand with a shovel. Slope the soil in the hole toward the street at a rate of 1 inch for every 100 feet.
Pour 2 inches of gravel into the hole and run over it with a mechanical plate compactor to firm up the base. You can rent a plate compactor at an equipment rental facility.
Install the plastic grid material on top of the gravel. Follow the manufacturer's instructions regarding the precise technique for the material you purchased, but generally you install the grids by laying them into the hole and interlocking the separate grids to each other. When needed, cut the grids to fit with a hacksaw.
Lay a thin layer of coarse cement sand on top of the grids, smoothing it out.
Mix topsoil and compost together in a 50-50 mix and spread it on the grids in a 2-inch layer.
Install sod on top of the topsoil/compost mix. Unroll the strips of sod on the mix, beginning at the bottom of the driveway. If needed, cut the sod with a utility knife. Water each strip of sod until it is soaked after you plant it.
Water the sod thoroughly every day for a week, then every other day for the following two weeks.