Purchase a fabric of your choosing at a sewing supply or arts and craft store, along with foam padding. In the alternative, you can use an old leather jacket or pillow cover for the fabric.
Place the fabric on the floor, laying the foam padding on top of it. Turn over one bar stool on top of fabric and padding. Trace around the bar stool's seat with a marker, creating a template on the foam padding. Then, pull the fabric up around the underside of the stool's seat and trace around it onto the fabric to get a traceable cut line.
Set the bar stool aside and cut both the fabric and foam padding with scissors, following the drawn outlines. Then, lift the bar stool used as a template. Place the fabric on the floor first and the padding on top of the fabric.
Pull on the edges of the fabric, stretching it over the bar stool's seat, holding the foam padding in place. Staple the edges of the fabric to the underside of the bar stool's seat with a staple gun, pulling it taut.
Cut off any excess fabric with scissors and turn the bar stool upright. You now have a covered a bar stool.