I've been asked this a few times. I'm not completely sure about all the keys for this. Looking back -- and also at the process today -- it seems to be a combination of things, and somewhat loosely connected.
The first thing to notice is what happens if you accidentally dial into the middle of a movie on TV you haven't seen for 20 years. How long does it take you to recognize the movie? And how often can you remember pretty much what is going to happen next? Then ponder that when you saw the movie the first time you didn't know you were going to be tested with just a few frames 20 years later!
There have been many studies over the years about just how good and detailed is visual recall. Much of the best recall is "prompted recall" usually via an image or some other sense (smell is a biggie).
You've also heard about Cicero's "mind palace" where when he was giving a speech in the Senate he would walk in his imagination around his villa and revisit parts of his speech that he'd associated with objects in his house.
This is also possible to do with ideas. It's a kind of relaxation from the parts of your brain that do general thinking (Kahneman's "System 2") and just letting the ideas be "configurational" (like images or sounds, where many can exist at the same time). A lot of the associations are kinds of analogies and metaphors.
In any case, we all have tremendous memories for some kinds of things, and it seems to be difficult to remember other kinds of things (perhaps things that are further from sense memories are more difficult). But it seems that a lot of the sense memory system is happy to remember enough "hybrid stuff" to then allow better recall of the more distant stuff.
One of the things I had discovered to a small extent in 3rd grade was that one can read "faster than actually thinking", and that a lot of the thinking would still be done. Looking back, I think this is like the kinds of background thinking we often do when we are working on a problem -- this seems to work also for reading. (It is also connected to how sight-reading in music is done (next comment).)
There's lots more, but one last thing here. Though I got to music early, I got to classical keyboards late -- in this case the organ -- and thus got a chance to watch myself learn to sight read three staves of music for hands and feet. (I found this quite a painful process for a few years, especially at my age.) But it has quite a bit in common with the mechanics of reading and remembering texts (with the addition of a lot of fine muscle memory that has to be taught what to do).
The essential transition is to gradually learn to detach from being "on the notes" to being able to see a few bars ahead (like what you do when you are reading aloud to someone), being able to perform with the meanings you just saw, while gleaning new meanings ahead and remembering them for the performance a few seconds later. It's basically a pipe-lined buffered process which anyone can learn to do, but which most do not learn easily (it was difficult for me).
If you can also tie the buffers to something that is in long term memory, you have a good chance of remembering it when something like it re-cues the memory. Most musicians wind up with a kind of double memory (they can remember the music more easily than the muscle movements). I think this also obtains in text reading and remembering.
The simple heuristic is "relax".