Do you have to press the “water drop” icon before you swim or when you are done, and then “wind” the stem until it goes away?

All pressing the "water drop" icon does it lock the screen to touch inputs, because water on the screen can register as random inputs. Winding the stem simply switches off the water mode and plays a tone to eject water from the speaker grill.

It isn't critical you press the water drop icon before swimming. However if you do forget, it's worth enabling the feature and immediately winding the stem afterwards just to ensure as much water gets removed from the watch when you are out of the water.

Personally I use the the water drop icon if I am swimming lengths, or surfing or whatever. If I'm just having a lazy day by the pool I tend not to use it at all.

The watch should automatically turn on the water lock when you enter the water,after your swim you have to turn it off yourself manually;

To disable Water Lock mode, simply turn your Digital Crown in one continuous motion. Your Apple Watch will then start beeping multiple times. This is to allow any water in the speaker grill to escape.