Bronte probably has given the best advice on this thread. However, good advice is usually not taken by people working in the finance sector as they're used to giving it rather than taking it. Furthermore, the same people are used to going up the ladder rather than down.
For a two storey house you need a single strong ladder, not an extension ladder which will sway and bend depending on your weight and actions. You'll need somebody to support the ladder at the bottom too i.e. somebody whose attention won't be broken by a phone ringing. You can rent such ladders, but you'll have to pay for delivery too as they are too long for support on the roof of a car. You need a light bucket for whatever is in the gutters. After you've cleared the moss etc from the gutters you can start cleaning the outside of the gutters/downpipes with hot water in which you mixed with Domestos or such like. Use a sponge too. You and the supporter of the ladder may need to wear some eye protection too.
Warning:- I don't believe there is a poster on this forum who doesn't know somebody who has not had a bad accident from using a ladder. Work carefully or your career could literally be cut short through a fast descent on your ladder.
Sorry for the black humour.