Public Transport options, especially Bus routes, seem to change fairly regularly. Look under the Roads and Transport section of the Surrey County Council website for up to date information. At the time of writing (November 2016) these are the best options.
The nearest station is Hampton Court. The service is approximately half hourly from Waterloo, through Clapham Junction, Wimbledon and Surbiton. It runs seven days a week, and takes about 35 minutes from Waterloo. The station is about two miles from the club, but the shortest route by foot or cycle is really too complicated to describe here: best to take a map.
If you take a cab from the station, and the driver doesn't know the location of the sailing club, tell him to go to the junction of Ray Road and Molesey Park Road: this brings you here where the rest of the route to the Sailing Club is signposted and obvious.
The 411 bus from the station stops about three quarters of a mile from the club: it will be easiest to get off at East Molesey High Street. From there follow the "finding us by car" directions.
Hersham Station on the Waterloo/Woking main line is about four miles away but as of January 2017 has no good bus links to Molesey. The direct cycling/walking route from Hersham is: turn right (roughly northerly) outside the station, go under bridge, past the industrial estate and the rugby club. (If you don't see these you've gone the wrong way). Keep walking until you see a right turn to Pool Road. Take this, it turns into Island Farm Road and you'll see Ray Road in about half a mile; turn right for the club.
The following routes come reasonably near the club:
411 - West Molesey, East Molesey, Hampton Courtand Kingston
This service runs about every 20 minutes on weekdays and half hourly on Sundays
461 - Staines, Thorpe Park, Chertsey, St Peter's Hospital, Ottershaw, Addlestone, Weybridge, Walton, West Molesey, Hampton Court and Kingston
This service runs hourly, seven days a week.
These stop about three quarters of a mile from the club: it will be easiest to get off at East Molesey High Street. From there follow the "Finding us by Car" directions. The Sailing club is signposted from here.