Burn the area where Roundup was used to clear away all of the dead weeds with matches. Rototill the area until the soil is soft. Using gloves, pick up any roots turned up by the rototiller and put them in a garbage bag and throw them away.
Level the tilled soil with a garden rake in a back-and-forth motion. Broadcast lawn seed using a hand-held seed broadcaster. Broadcast fertilizer in the same fashion.
Cover the broadcast seed with a thin layer of straw 1/2 inch thick. Lay perforated soaker hoses over the area and keep the area wet until lawn seeds germinate and grow. Reduce watering to once a day as soon as the grass is 2 inches high.