Waterloo --> Jubilee Line towards Stratford --> Canning Town --> DLR towards Woolwich Arsenal --> London City Airport.
Easy peasy and lifts throughout.
Taxi will be a nightmare route out to Dartford, then either in on A2 to Blackwall Tunnel or the A13 after the Dartford Tunnel. Couple of hours or more from Guildford.
Trains are quicker and cheaper.