Hi, Jane. It's best to do this on a nice warm day when your furniture will dry quickly but here are the steps. Was the furniture with a mix of one cup of household bleach (like Clorox) per gallon of water to kill the mold. Rinse and wash with a mix of one cup of white vinegar per gallon of water to neutralize the bleach. Rinse and let dry. You may want to scrub the bleach mix into the wood but this is determined by the amount of mildew. Do not neglect the neutralizing step ans that will prevent problems for you or your guests when they sit on the furniture. The pieces will normally have the nice gray color and will not maintain a "new wood" look for long, no matter what you do. Ultraviolet light causes the deterioration. Marine or spar varnish offers some protection but also adds a yellowish hue. This may peel so I favor just leting the teak weather to it's natural weathered color.