The process of figuring out how a dish you are served (typically, at a posh restaurant) is prepared, by the application of observation, smelling, manual disassembly and of course tasting. By analogy to reverse engineering, and given the analogy between engineering (design of a construction or product which may subsequently be manufactured, perhaps by people other than the engineer) and cuisine (design of a meal or dish which may subsequently be cooked by the chef or other people, e.g. his sous chefs).
This takes some practice. As with any engineering, you need to be pretty familiar with the process you're duplicating. You will need to distinguish and identify individual ingredients, and then come up with a reasonable method. To practice the former, try guessing all the ingredients in stuff your friends and relations cook up. This will sharpen your senses (and increase your appreciation of fine cuisine -- assuming what you're being served deserves that distinction). Picking out one flavour from all the rest is not always easy (try differentiating spices in an Indonesian curry), so see if different main ingredients may have picked up different tastes, making your job easier.
You can practice guessing the method too, but in my experience to do that you really just need to try out many cooking styles. You can then compare the dish before you to various techniques you are already familiar with, and at least come up with some requirements (e.g. more liquid than a stir fry, more finely chopped than you can get with a cleaver, creamier than when you do this-and-that...). Visual hints are a great help here. Is the exterior of your steak charred (indicating high heat), or damp (cooked in liquid), or perhaps recognisably marked by some grill rack etc.? If your Jerusalem artichokes are sliced or shaped in an unusual way, can you find bits which give away the utensil used? And so on.
Of course, the dish's title can drop some great hints (Pan Roasted Platypus Brioche served with Kiwi Coulis Flambee is quite a giveaway). And in a pinch, although this is really not done, there are certain discrete inquiries you can make of the waiter, the maitre d' or even the chef.
Finally, you will almost certainly need to experiment. If you enjoy improv cooking, the worst that can happen is you'll come up with your own original recipe. In a way, that's how I got to invent Green Calamari Rings. If memory serves me right, my Cauliflower Soup is a reverse-cuisined recipe, at core, although one vital trick is without a doubt original. Remember that many reverse engineered products are definitely superior to the original.
An interesting challenge, though one hardly necessitated by copyright law, is to attempt the clean room reverse engineering, made (in)famous by the Compaq PC cloning. The dirty team would eat out at the fancy restaurant, chat up the waiter, etc. They would then write a detailed review of the meal they had, possibly of the snobbish restaurant guide type, without any mention of cooking technique. The clean team, having no contact with the dirty team except by way of this review, would come up with the detailed ingredient list, and of course the all-important method. If I ever try this, I will report it here. /msg me if you attempt this, or if you've done it before.