Godalming is served by South-West Trains on the London Waterloo to Portsmouth Line. There is a relatively frequent service throughout the day. Journey time is around 45 minutes to Waterloo on the stopping service. Godalming is two stations from Guildford, where you can get an express to Waterloo in around 30 minutes. You can check connections and fares on thetrainline.com
From Guildford - 2 stations away - you can get a direct train to Gatwick airport in about 50 min.From Woking - 4 stations away - you can get a bus to Heathrow 50 min, and a direct train to Southampton Airport Parkway station 50 min.