One way to avoid spooking an owl is to not approach it rapidly. If you see someone watching it safely from one side, go slowly to the same side person is viewing it from.
So the moral of the story is do not approach the owl quickly, or surround it.
A second way not to spook a snowy owl is do not talk loudly or yell around wildlife, not just snowy owls. I saw someone do just that and the snowy owl flew off. I had the opportunity to follow a barred owl family spring through summer last year. If you are quiet, they will allow you to observe from a safe distance. Whenever other people were talking in the woods or were walking a dog you had less luck seeing them.
In addition, if it is known there are snowy owls on the beach do not walk your go there. Two beaches I found snowy owls on had signs saying no dogs. However, that was not being followed. Not sure if it only applied in the warmer months. I saw an owl spooked a third time because someone walked a dog not far from it. The owl took a few short flights to avoid the situation.
Also, keep a distance where you are not stressing the owl. If the owl is stressed back away. Jones Beach had signs saying keep at least a 100 feet away. Those signs were down last time I was there. I would say that is a good distance to be safe.
Snowy owls are beautiful birds to watch. Respect the animals and other people, and you will enjoy the experience.