Waterloo to Oxford Circus by Underground on the Bakerloo line, then Victoria Line to King's Cross. This route is suggested because there is a very easy interchange between trains at Oxford Circus which saves time and effort compared to the alternatives.
Waterloo to Warren Street on the Northern Line, then Victoria Line or bus 10, 73, 390 to King's Cross
Waterloo to Leicester Square on the Northern Line, then Picadilly Line to King's Cross