To clean fabric dining chairs at home, vacuum the chairs to remove any loose dirt and debris. Then, create a cleaning solution by mixing mild detergent with warm water. Dip a soft cloth or sponge into the solution and gently scrub the fabric, focusing on any stained or soiled areas. Rinse the cloth or sponge frequently and continue until the entire chair is clean. Finally, allow the chairs to air dry or use a fan to speed up the drying process.