Others may come up with better options involving things like buses (which I know little about!), but I would take the train from Gatwick to Victoria and then the Underground from Victoria to Waterloo. You can save a bit of money by using the ordinary train rather than the Gatwick Express, and you should be able to buy a through ticket from Gatwick to Waterloo (i.e., one which includes the Underground)

PS Looks like two of us were replying at the same time. Cutting the corner at Clapham Junction sounds like the better option!