Water the entire lawn to a depth of 1 inch. Allow the soil to dry out just enough that it's still moist, but not soggy, which should be about two days. The soil should be just moist enough to pack when tamped.
Position a motor-powered core aerator in any corner of the lawn. Turn on the aerator according to the directions of the particular model.
Walk the aerator in a straight line along the edge of the lawn. Pivot 180 degrees at the end of the lawn and walk the aerator in a second straight line, directly beside the first. Continue this process until you have aerated the entire section of lawn.
Return the aerator to the original starting position. Walk the aerator across the entire lawn, using the same row-by-row method, but go in the opposite direction.