I'll try to explain UDT by dividing it into "simple UDT" and "general UDT". These are some terms I just came up with, and I'll link to my own posts as examples, so please don't take my comment as some kind of official position.
"Simple UDT" assumes that you have a set of possible histories of a decision problem, and you know the locations of all instances of yourself within these histories. It's basically a reformulation of a certain kind of single-player games that are already well known in game theory literature. For more details, see this post. If you try to work through the problems listed in that post, there's a good chance that the very first one (Absent-Minded Driver) will give you a feeling of how "simple UDT" works. I think it's the complete and correct solution to the kind of problems where it's applicable, and doesn't need much more research.
"General UDT" assumes that the decision problem is given to you in some form that doesn't explicitly point out all instances of yourself, e.g. an initial state of a huge cellular automaton, or a huge computer program that computes a universe, or even a prior over all possible universes. The idea is to reduce the problem to "simple UDT" by searching for instances of yourself within the decision problem, using various mathematical techniques. See this post and this post for examples. Unlike "simple UDT", "general UDT" has many unsolved problems. Most of these problems deal with logical uncertainty and bounded reasoning, like the problem described in this post.
Does that help?
ETA: I notice that the description of "simple UDT" is pretty underwhelming. If you simplify it to "we should model the entire decision problem as a single-player game and play the best strategy in that game", you might say it's trivial and wonder what's the fuss. Maybe it's easier to understand by comparing it to other approaches. If you ask someone who doesn't know UDT to solve Absent-Minded Driver or Psy-Kosh's problem, they might get confused by things like "my subjective probability of being at such-and-such node", which are part of standard Bayesian rationality (Savage's theorem), but excluded from "simple UDT" by design. Or if you give them Counterfactual Mugging, they might get confused by Bayesian updating, which is also excluded from UDT by design.
Thinking about this.
ErinFlight said:
Thinking about it, I realized that this might be a common concern. There are probably plenty of people who've looked at various more-or-less technical or jargony Less Wrong posts, tried understanding them, and then given up (without posting a comment explaining their confusion).
So I figured that it might be good to have a thread where you can ask for explanations for any Less Wrong post that you didn't understand and would like to, but don't want to directly comment on for any reason (e.g. because you're feeling embarassed, because the post is too old to attract much traffic, etc.). In the spirit of various Stupid Questions threads, you're explicitly encouraged to ask even for the kinds of explanations that you feel you "should" get even yourself, or where you feel like you could get it if you just put in the effort (but then never did).
You can ask to have some specific confusing term or analogy explained, or to get the main content of a post briefly summarized in plain English and without jargon, or anything else. (Of course, there are some posts that simply cannot be explained in non-technical terms, such as the ones in the Quantum Mechanics sequence.) And of course, you're encouraged to provide explanations to others!