The first thing to note about Fallout 4 is that it is not a story. It is rather a collection of stories, all contained within one single overarching frame. In order to read these stories as they are, in their manifold, it is important to acknowledge them as such: many.
There is an argument to be made that this multitude of stories gets in the way of the main story. Ostensibly, the protagonist is on an emotionally intense quest to recover their kidnapped child. In terms of gameplay, the player spends weeks and months of gametime doing absolutely everything but searching for that kid. After having become a raider boss who deliberately and systematically enslaved vast swathes of the countryside, the sudden emotional intensity of finally being reunited with the prodigal son is, to understate it, sudden. There is a main story, to be sure, but there are also so very many other stories going on that it becomes something of a sidequest. As it were.
That is a possible avenue of critique. But it is also a sidetrack from the assertion that you can read Fallout 4. Which is a more interesting assertion. Not least because it implies that the game is readable, and that it somewhere along the line had authors, who made choices as to what went where.
A first thing to note is that (almost) nothing is where it is by accident. This tells us something important. This tells us that if we pay attention, we can glean information as to what happened to the places we visit as we explore them. The placement of corpses, the layout of buildings, the textual residues on terminals (which, as an aside, are a nice return of the epistolary genre), the kinds of enemies encountered, and the various missions which brings you to these places in the first place. All of these things tell us something, if we but pay attention. It is environmental storytelling, and it is a lot of it.
The corpses, especially, tell many tales. They speak, ever so silently, about what happened before you found them. Some of them are from before the war, and suggest at the social processes taking place on the day the bombs fell. Other corpses are more recent, and subsequently tell of more recent events. Pay attention to where you find them, how many of them there are, and if there are items nearby which suggest particular courses of events. There is a suggested grammar to the corpses you find, in that skeletal remains are implied to be prewar, while meaty (to use a word) ones are recent. It is also implied that teddy bears represent the younger pre-war generations, but this is not universally applied.
At this point, you probably have questions, such as: why are the terminals still working after all this time without an apparent power source? How come no one has removed the corpses in the hundreds of years between the bombs falling and you finding them? Why are you apparently the first person to visit some of these places, when there are evidently people moving about mere hundreds of meters away?
These are good questions, and rather than answer them, you will have to either suspend your disbelief, or see the game as a written artifact. Everything is where it is because you are meant to find it there, and you are meant to see it as it is presented to you. The ghoul you find in the director’s office is in fact the director, and he has been in his office all these years, waiting. The nearby terminal that tells his story is indeed telling the story of the feral creature you just witnessed. A story that you, the player, is the endpoint of, and that you, the reader, is a witness to.
Fallout 4 is many things, and one of them is a balancing act between player and reader. It is possible to blast through the game without paying too much attention to detail, and still have a good time. Reading is not a requisite for playing. But a lot of effort went into making a great many places readable, both in themselves and in reference to the earlier iterations in the Fallout series. Should you effort to acquire a literacy in reading the results of these efforts, you will find yourself back at the start of this text: with the realization that there is not a story, but many stories. In this game and in life both.