Check carefully to make sure you are not disturbing any live spiders, particularly if they are either black widow or brown recluse spiders.
Use an aerosol insecticide for flying insects or a residual spray such as crack and crevice spray to debilitate the spider, but do not spray more than required for fear of ruining the material of the sofa.
Take the cushions outdoors and clean them with a powerful suction vacuum cleaner.
Wash the cloths either by hand or in an automatic washing machine.
Vacuum the entire sofa and pay particular attention to creases and crevices in the material. Upturn the sofa and vacuum the underneath as well. Use the vacuum to remove any visible spider webs, as these may contain eggs.
Sprinkle an insecticide dust that is manufactured for spider control on the underside of the sofa. Place gloves on your hands and rub the dust into the material. Turn the sofa right side up and sprinkle insecticide dust over the entire sofa, paying particular attention to the creases.
Return the cushions to the sofa and sprinkle insecticide dust on them as well.
Vacuum the sofa on a regular basis to make sure no new eggs have been laid.
Place caulk in all cracks and crevices around doors and windows to prevent spiders from entering the house, after you have removed the eggs. Install tight-fitting screens to doors and windows, as an extra precaution.