Identifying the GPU, for example, is based on recognizing that there are eight repeated elements within it, and matching that with the known fact that there are eight GPU cores.
The chip design and fabrication firms have their own internal RE divisions mostly to QA their own chips. They do competitive RE, but its often less expensive for them to get a subscription to TechInsights. Economies of scale and all that.
In terms of how its done, its very proprietary. I can tell you it involves clean rooms, ion beams, electron microscopes, chemistry, and bleeding edge software.
If you want to come work for us (its enjoyable, you should :) ) check out our careers page. We are hiring like crazy in many positions.
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How far can someone with time and money go towards reverse engineering a chip from such pictures?