I can understand how they steer a sternwheeler but steering a sidewheeler has me mystified. Seems to me it would always want to turn toward the paddle sideof the ship.
Aren’t there paddles on both sides?
Yep
So anyway, how is it steered? Are the paddles independently powered, allowing one side to be stopped or run in reverse, to turn the vessel, or are they on a common axle?
They steer the same as a sternwheeler with the ability to independantly rotate their axles to augment it.
Paddle boats often employ both bow and stern rudders, and sidewheelers are no different, but they are more manuverable (though wider) due to the addition of differential thrust.
Hmmm
funny.
I can still clearly “see” the mental picture from a long forgotten book of a sidewheeler that only had 1 wheel.
Its been more years than I wish to think about that I’ve wondered how that thing got around.
Thanks all
There’s this old joke:
There’s a journalist, a zoologist and a mathematician going north into Scotland for the first time, on a train.
Through the train window they see a cow, facing the same direction as the train.
The journalist thinks: “Ahhh, cows in Scotland are brown”
The zoologist thinks: “Hmm, so you *do * find brown cows in Scotland”
The mathematician thinks: “There’s at least one cow in Scotland that is brown on one side”
Are you a mathematician, justwannano? 
It should be possible to do this, with a large enough rudder to counteract the offset thrust. It’s the seme with a solo canoe - you only paddle on one side, so each stroke causes the canoe to turn in one direction. So at the end of each stroke you need to use the paddle as a rudder to turn it back.
That would be the “J” stroke, I believe.
Sorry, that should be:
"The mathematician thinks: “There’s at least one cow in Scotland that is brown on at least one side”
Gondolas are also driven (sculled) by a remo that’s fixed on one side. Gondolas are logitudinaly asymmetrical to counter the sideways drift.