Grass and other plants stop growing under a pine tree for two primary reasons. One is the shade; the other is the extra acidity from pine needles that drop onto the soil and decompose. Grass grows poorly in acidic soil, so you'll have to neutralize the soil under your pine trees. This is easily accomplished by adding an alkaline soil amendment.
Rake all needles, bark and any wood chips from around your tree, using the rake. Needles and wood add acid to the soil under the tree.
Run an aerator under the tree. The aerator should be set to a depth of 1 to 1 1/2 inches. Use care not to damage roots close to the surface. Use the aerator from the tree's drip line in; the drip line is where the tree's longest branches extend to.
Spread lime in the aerated area, using a lime spreader. Use 25 lbs. of lime per 1,000 square feet. A circle with a radius of 10 feet encloses an area of approximately 315 square feet.
Rake fallen pine needles so they do not add new acid to the soil.
Add approximately 25 lbs. of lime per 1,000 square feet each spring, using the lime spreader.