Put on garden gloves and use a shovel to get up most of the weeds by their root. For stubborn weeds, spray a weed killer directly around the bottom of the fence line and posts.
Spread fertilizer around the bottom of the fence and posts. This helps to heal the damage to the soil caused by the weed killer and encourages grass growth in these areas. After fertilizing, water the area for a few minutes by hand.
Plant or spread grass seed along the fence line and around fence posts. Do this with a seed spreader, available at hardware stores, or by hand. Sprinkle the seed along the area and gently work it under the soil by hand. Make sure you don't plant the seed more than 3 inches below the surface so the grass has enough sunlight to grow. After planting the grass seed, water the area again, by hand.
Repeat watering the new grass seed daily for three weeks, until grass begins to grow in place of the weeds.