"Put your hands together so that they match up exactly, as if you were praying. [there's a picture]. Choose one of the three compatibility dimensions ... Now think of someone you know well ... Try to get a felt sense of how compatible you and that person are on the dimension you've chosen. .... Play the mental video you have of that aspect of your relationship with that person. Visualize key incidents that seem to exemplify that dimension. As you do, pay attention to how your body feels. ... keeping your hands together, rotate them with respect to each other until it feels like the angle between your hands matches your felt sense of how alike or different you two are on that dimension"
There's more detail and development, but this is basically trying to get you listening to your less-verbal/more-feeling side of yourself (get people out of denial, out of rationalization).
Hamburg has a taxonomy of compatibility: Practical, Sexual, Wavelength. He assesses couples using the hand rotation trick for compatibility based on a bunch of components of the three dimensions of compatibility. So this is an interesting variation on the more typical approach: fill in a five choice scale for a bunch of descriptions on a written test.
Hamburg has a theory of what kind of compatibility works and what doesn't, based on his clinical experience. Hamburg believes that open relationships cannot work because he has seen tortured looks on the faces of people who were cheated on. Needless to say, I find that perspective a little troubling. Thinking, oh, walkitout, that's a bit of an overreaction?
"An option that some of us choose is to marry but not be monogamous. That is not an option I can recommend. It's not my job, as a psychologist, to give you a moral argument about why infidelity [sic] is bad. You have enough other people moralizing at you about that. I'll just share a clinical observation: In my work with torture survivors and with people who have lost a child, I have seen the face of anguish. The only other people in whom I've seen anything even approaching that anguish are people who have been cheated on by their husband or their wife."
Equating nonmonogamy with infidelity is repulsive. Equating nonmonogamy with cheating is disgusting.
There are a lot of useful things in this book, that could be useful to those in poly relationships: the ideas that compatibility isn't a unitary scale but has parts and you might be compatible in some areas but not in others, and some incompatibilities cause one kind of problems and other incompatibilities cause very different problems -- these are great ideas. But they are so embedded in a monogamous perspective (and honestly, the heterocentricity is a bit wearing as well) that I cannot recommend this book and found it difficult to finish even as I was finding more details that I thought were useful and insightful. YMMV.
ETA: Oh, and please don't sit around worrying about my marriage or anything like that. That's not why I'm reading couples counseling books. I'm reading couples counseling books because I realized whenever someone I knew was having trouble, I was recommending Gottman, and I thought there surely must be better stuff out there since I've known about Gottman for a while. If you've found really useful LTR maintenance/fix-it books other than Gottman (or Hamburg, or that horrifyingly awful _Passionate Marriage_ thing that people were all over for a while), I'd be interested to know which ones you found useful. Think of it as spreading the word generally, so as to make best practice available to those in need.