Work carefully when sanding teak furniture so you don't damage it. It's not a good idea to use a power sander, which could make the sanding process too rough. Holding a piece of carpentry sandpaper (fine grade to medium-fine grade), gently sand any areas that require attention. When the areas being sanded first appear to be smooth, stop sanding. Don't overdo it.
Mix equal amounts of water and detergent. Then mix one part bleach with three parts of the detergent-and-water mixture. Use the bristle brush to clean the furniture with this solution. Again, be sure not to brush extremely hard or for too long on any area.
Purchase teak cleaner if you desire. This could be more effective than the homemade mixture, but will cost more. Teak cleaner can be found on a number of websites (see Resources). Prices vary, so do some research before purchasing. Teak cleaner is also available wherever teak furniture is sold.