First, I either sit down in the river or float in an eddy. I stay in the water, preferably in good cold water, to lessen the pain. My knees are bent.
I clasp my hands and lock my fingers together.
Then, I grab whichever knee is on the same side as my dislocated shoulder with my clasped hands, and lean back. This extends my arm out enough for my shoulder to slide back into socket.
Takes about 5 seconds.
The longer my arm is out of socket, the worse the pain gets, until it is unbearable. So the quicker I get things right the better.
By setting my own shoulder back in socket, I risk nerve damage and/or blood vessel damage.
However, in a wilderness setting like a remote river run, I choose to alieviate the dislocation and pain, so I can get to safety quicker.