Waterloo station is exactly where you should head for if you're going to the 'South Bank'. It's very close to the Royal Festival Hall, the British Film Institute, the Queen Elizabeth Hall, the National Theatre and the London Eye. Tate Modern and Shakespeare's Globe are within easy walking distance.
There are lots of river services, running from various piers - but most of them are on the north side of the Thames. The nearest to Waterloo is Westminster Millennium Pier. It's a fairly easy walk from Waterloo but (because of heavy traffic levels) it's not particularly pleasant. It's probably better to take the Jubilee Line, for one stop, northbound to Westminster station.
From Westminster Millennium Pier there are river services to Kew, Richmond, Hampton Court, Greenwich and the Tower (among other places). Details of times and prices are in this guide:
http://www.tfl.gov.uk/assets/downloads/river-g uide.pdf
Chris