I'm not pretending this will work for everyone, but here's what worked for me.
Phone was dropped into a clean toilet and immediately recovered, so it was in the water for no more than a second or two. Screen was still on, so wiped with a towel and my next thought was to switch the phone off while I decided what to do. Unfortunately at this point it started flashing and misbehaving. After a few seconds, it would settle down again and the screen would go blank, but same problem every time I attempted to switch it off.
With my old phones I would have simply removed the battery, but not an option with the S6.
I did read some of the ideas here, but was quite wary of dismantling it myself.
In the end, I removed the SIM card and blew hard into the slot where it goes. A few droplets of water appeared around the camera, so wiped these away. Repeated this a few times until no more water droplets appeared. Then I got out the hair dryer, switched it to hot and basically heated the phone all around, paying particular attention to the slot where the SIM card goes. My hope was to simply evaporate any dampness still in the phone. I did this for a few minutes and after a couple of attempts, the screen was showing it's usual display. At this point I was able to power the phone down using the switch. For good measure I left it powered off overnight.
Next time, I switched it on, all was working ok again. I have a suspicion it would have worked straight away, but didn't want to take that chance.
I know I got lucky and this may not work for everyone, but it did work for me and may work for you too if you are able to act quickly.