Just because there is a layer of asphalt on the ground does not mean you cannot change it into a lawn. Grass grows as long as it has enough soil for nourishment and water for moisture. While eliminating the asphalt first is the best option, if that is not possible, a lawn will grow over asphalt if the paving material is first covered with soil. Sod is the practical choice for a quick lawn, both for the quick green, but also to hold soil in place.
Bring in 4 inches or more of fill dirt to form the base for growing sod over asphalt. Grass roots will penetrate about 4 to 5 inches down and should not be able to reach the asphalt if the layer of soil is thick enough.
Cover the fill dirt with another 4 inches of topsoil to form the growing surface for the sod. Smooth it out well with a rake to make a level growing surface.
Moisten the layers of soil with water until the soil 6 inches down is damp so the roots of the sod will access the water easily and readily. Allow time for the water to percolate down so that you don't create a muddy surface when you are laying the sod.
Lay the sod over the damp top soil. Fit each start of a roll of sod up close to the end of the last roll. Keep seams alternating throughout the lawn. Use a roller to press the sod into the soil.
Water the planted sod immediately after planting. Continue to water the area every day for the first week until when you tug gently on a section of sod, it resists. Water as needed during the growing season to supplement low rainfall amounts.