How does continuity work?
Well, that's a simple enough question, right?
TL;DR: coordination behind the scenes, plus more willing suspension of disbelief than usual. And, it doesn't always work as well as it could.
Most events may involve a semi-permanent change of status for a couple of characters, but most of the characters involved won't have changed significantly. Take a relatively recent event, Civil War II. Coming out of that, several characters had status changes:
- War Machine
- Iron Man
- Guardians of the Galaxy
- Captain Marvel (arguably)
For those characters who had on-going books at the time, the book reflected the changes arising out of the event. Sometimes that happens somewhat out of sequence. Often, in those cases, a warning of some sort will be included on the first page (or, for current Marvel books, the summary page that comes before the first story page, usually). For instance, "This story takes place before Frog-Man #675."
If the character's own title is actively participating in the crossover, then usually someone at an editorial level at least has some idea of the order in which the various pieces of the event happen. Again, where critical, if the books may not be published in the same order as they occur, there may be a warning as noted above. In general, of course, you know that the events in the character's book that happened before the crossover issues happened before the character was actively involved in the crossover, and the ones after take place after their primary involvement in the crossover.
Where a specific character involved in a crossover stars in a book that's not involved, and the character was notably affected by the crossover, then usually the writer will address whatever status change happened. If the Usurious Underwriter had his right arm chopped off during a crossover, they won't just suddenly start showing him in his comic with no right arm without explaining what happened.
If the character was not notably affected, then the team on the character's own book may not even mention the crossover. You'll be left to assume that it happened at some point in the character's story where there's a break point. This usually happens between issues, but can occasionally happen within an issue.
Just to plainly state a fact that's alluded to above, ou must realize that individual comic books do not necessarily occur in the order they're published. If a character is needed for a crossover, but is in the middle of a tightly woven story in their solo book that's ultimately going to run for a year, then their year-long story may happen before or after the crossover, even though the crossover was published right smack in the middle. Even for books involved in a crossover, they may not be published in the exact order in which they happen (hence the "This story takes place before/after" notes mentioned earlier).
Note that this doesn't only apply to crossovers. Most of the time, minimal effort is taken to coordinate a character's activities in a solo book with their activities in a team book. Canonical examples would be Wolverine and Spider-Man.
During the time when Wolverine was an Avenger and an X-men and had his own solo book, and acting as the headmaster of a school, and making guest appearances in various other places, there generally wasn't any sort of plan laying out how all this was possible, or what order it happened in - except, as noted above, when all the books were involved in crossovers (for instance, Avengers Vs X-Men, which involved all his team books, but not his solo book). Most of the time, it wouldn't matter if New Avengers 1-5 happened before or after Wolverine and the X-Men 5-8.
For over 20 years, Spider-Man was featured in 3-4 monthly comics (and that was before he was in a team!). Throughout the 1970s and 1980s, Amazing Spider-Man, Peter Parker, the Spectacular Spider-Man, and Marvel Team-Up (later replaced by Web of Spider-Man) were published monthly, with only occasional references to each other. Again, changes of the status quo (the advent of the black costume; his marriage to Mary Jane Watson; changes to whether he worked for the Bugle or not) were coordinated amongst the three titles, but individual storylines were not. In a given month, you might find the second part of a three-part story in Amazing, a self-contained story in MTU, and part 5 of a six part story in Spectacular. In general, it wasn't assumed that all readers would read all the various titles, so no strong effort was made to string them all together in a logical order.
Note that this hasn't always been true. In the 1990s, DC's Superman books actually included a number indicating the order they happened in (which matched the published order), even though there were 4-5 titles involved, each with a different creative team. However, a lot of stories actually ran through all the titles, as opposed to having longer multi-part stories that ran through just one title, done by just one creative team (this did happen sometimes, but it was done without true cliffhangers at the end of each issue, since the character would be doing other things before the story resumed). The disadvantage to doing things this way is that, if someone was only interested enough in Superman to buy one title a month, they'd eventually drop that one title, because it was too difficult to understand what was going on from one issue to the next.
As mentioned at the top of this article, Marvel (and, I believe, most other publishers with strongly connected books) tends to have editorial teams that handle a set of related books (you'll see references to the X-Men office, the Spider-Man office, etc.). This allows some degree of coordination. Where characters are used across multiple offices, significant changes of status quo get communicated between teams. An example - the young Cyclops seen in both X-Men Blue and Champions was recently written out of Champions, due to impending changes to the X-Men books.
As I've stated, this hasn't always worked as well as it could.
Sometimes, the creators did something about it.
In the late 1970s, Thor had a lengthy storyline (lasted almost a year and a half) where he was in space.
During that time, he made a couple of spot appearances in the Avengers.
I'm not certain if it was planned all along, or something that only bothered the writer or editor after a while, but in the next big Avengers storyline (usually known as the Korvac Saga), it was established that Thor had been pulled out of time/space by the Collector (to ensure that he could later successfully collect all the Avengers, without any pesky holes due to death when going up against a vastly more powerful entity), then replaced back where he belonged, with no memory of the Avengers' adventure.
Sometimes, no one did anything about it (warning: I'm about to talk about a personal pet peeve that's bothered me since the 1970s).
In the mid-1970s, the Fantastic Four had an long-running storyline where Reed Richards (Mr. Fantastic) lost his powers. This started around issue #164; he didn't actually lose his powers until issue #177 or so; and, he regained his powers in issue # 197 (issue #s pulled from memory).
Ironically, during this same time, Ben Grimm lost his powers, reverting from the Thing to an ordinary human (something he welcomed). This covered a much shorter period of time: he became human in issue #167; he got an exoskeleton suit in #170 that gave him the strength (and appearance) of the Thing; and, in #175, he lost his human form and became the Thing full-time again.
At that time, the Thing starred in a comic book named Marvel Two-In-One, where he teamed up with some other hero in each issue. There was even a crossover between Fantastic Four and Marvel Two-In-One just after he got the exoskeleton suit. After that, we saw Ben in the exoskeleton for a few issues. Then (after he was the Thing once again), there was a lengthy storyline (running for about 9 months), where Ben travels to England, bringing his girlfriend Alicia Masters with him. You can tell he's back to being the Thing, because he does some depressed moping about it.
At the end of this storyline, Mr. Fantastic guest-stars. At this point in the Fantastic Four, he's still powerless. However, in the story, he can still stretch - from his thoughts, it's clear this is set before he lost his powers.
So, it takes place between when Ben became the Thing again, and Reed lost his powers. Unfortunately, that means between FF 175 and 177 - and there's no break points in that story. The FF come back to Earth from off-planet, fight with the Impossible Man, and then go to their headquarters, where they're immediately captured by enemies. It just can't fit.
When that happens, you basically just have to choose to ignore it - to suspend your disbelief further than usual. And, clearly, for some of us, it's harder than for others :-).