Place a small screwdriver or other thin, rigid object against the pin holding the valve handle to the valve body. Tap the end of the screwdriver or object to remove the pin from the handle. Pull the handle off the multiport valve. Remove the metallic spring and the Teflon washer from the valve body.
Unscrew and remove the screws positioned around the top of the multiport valve body. Pull the valve's cap off the body to expose the spider gasket.
Pull the old spider gasket off the interior of the multiport valve. If the spider gasket refuses to move, use a flat screwdriver or smaller pocket knife to peel the gasket away from and off the valve.
Coat the replacement spider gasket in an O-ring lubricant such as Aqua-Lube, or a general lubricant such as petroleum jelly. Set the spider gasket down onto the interior of the valve, matching up the legs of the gasket with the legs on the valve interior.
Place the valve cap on the valve body. Set the Teflon washer and metallic spring on the valve in the same position as they were in before removal. Place the valve handle over the washer and spring. Hold the handle down and insert the pin into the handle. Tap the pin with a hammer to fully insert it into the handle.