Let's start with a simple eye exersize. Hold a finger up half way between your nose and the computer screen. When you focus on your finger you will see two screens. When you focus on your computer screen you will see two fingers. Now for the exercise, switch focus back and forth between your finger and the computer screen a few times. That's the eye motion you need to view a stereogram.
Now look at the sterogram below and you will notice the pattern repeats somewhat from left to right. All sterogams have a repeating horizontal pattern, that's what makes them work. If the picture did not contain a hidden image, the pattern would repeat exactly across the page. The hidden image is contained in the errors as the pattern is repeated.
Ok, enough background info, here's how you view the hidden image. Find some feature that you can recognize in two adjacent patterns. Look half way between the two features. Now look through the monitor at the wall behind, work with me here. You should see two copies of the stereogram that move from side to side as your focus point moves. Here's the tricky part. Adjust your focus point to slide the images around until the two adjacent patterns line up. I find that tilting my head slightly back and forth helps. Maybe my head isn't screwed on straight. When the patterns line up your brain will lock on and see one pattern. The differences in the two patterns are interprited by your brain as 3D information, revealing the hidden image.