This is the best instruction I've read so far on seeing them. I'm fine with cross-eye stereograms, so lining up to 3 dots was easy. What you described as "stabilizing" your vision once you've focused is what I normally do with cross-eye images to look around.
In this case, I can stabilize, but I feel like I'm still seeing the inverse of what I should be seeing. The hemisphere looks like it's carved into the image (with various bands that I assume are shading). The very center looks like a hole was cut out and I can see "behind" the hemisphere. I assume this is supposed to be a highlight and the nearest point to me, but I see it as the furthest.
Yeah, it's inverted for me too (hemisphere looks carved into the screen). chubasco's comment seems to indicate there's a way of looking at it that goes the other way (and that my technique results in a backwards image), but IDK — the above is the limits of what I know.
Firstly: play around with the zoom. I have a much easier time with these at smaller sizes. Second, lean in close to your monitor, so that your eyes are straining a bit to keep the image in focus. Let your eyes "relax" out of focus. At first this might seem the same, but you're getting your eyes to effectively un-cross. Line up the three dots and you should now see the hemisphere in front of the plane, rather than as a cutout.
In this case, I can stabilize, but I feel like I'm still seeing the inverse of what I should be seeing. The hemisphere looks like it's carved into the image (with various bands that I assume are shading). The very center looks like a hole was cut out and I can see "behind" the hemisphere. I assume this is supposed to be a highlight and the nearest point to me, but I see it as the furthest.