How is a seaplane steered on water?
Seaplanes mostly have water rudders that are used at lower speeds and are retractable (actually, they tilt out of the water flow).  At higher speeds, like takeoff runs and landings, high speed taxis, they are retracted and the primary means of steering is the plane's rudder.  Water rudders are connected to the regular rudder pedals.  

Airlerons can also be used to steer a seaplane on the water by creating differential lift and drag (since most ailerons don't deflect symmetrically). 

Doors can be used to steer by opening one or the other, creating drag on one side or the other.  I have seen a C-150 pilot do this in the air, as well.  Flaps, which create symmetrical drag, can be used to assist in slowing down but they're not useful for steering.  

Seaplanes have no brakes other than the drag of the floats in the water, so a seaplane pilot won't approach a dock at a perpendicular angle.  Instead, they will land along side a dock and then jump out onto a float and then to the dock, rope in hand.  

Seaplane pilots also carry oars, which allow them, yes, to paddle, steer, and stop the plane. 

So seaplane pilots have a number of tools at their disposal to steer the plane on the water. You can also read through the FAA Handbook for seaplane operations.

It does require some coordination!