First off, make sure to read my general rules of time travel in a Many-Worlds model ... here. Or you can just accept the synopsis here: you can only travel forward in time along your own timeline (can't go to other branches); you can only travel backwards along your timeline (backward along the branches); when you go back, it automatically creates a new timeline (a new branch); and tethers are the only way you can return to an original timeline.
Okay, we will begin with a simple timeline. This is the line on which all of the first 21 movies occur, and it looks like this:
Looks exciting? We'll call this Timeline Zero.
In 2023, the first time travel trip has Hawkeye going back to visit his family farm. He doesn't stay long, and he doesn't really change anything. Technically, he does create a new timeline (branch), but it would look very close to Timeline Zero. So, we'll just ignore that trip.
Once they know time travel works, the Avengers and friends split up into three different teams that go back to three different times. We'll handle the easiest one first ... Thor and Rocket going back to Asgard.
Arriving in 2013, Rocket steals the Ether from Jane and gets chased by folks while Thor talks it up with Mom. Thor then summons Mjölnir. The fact that things happen differently is evidence that the Many-Worlds model is in effect. In other words, we have a new branch. We'll call this Timeline Thor-2013.
Thor and Rocket then return to 2023 Timeline Zero thanks to the "GPS" tether platform combination that Tony Stark created. Without the tether, Thor and Rocket would have been stuck in Timeline Thor-2013.
This is what our time map looks like now:
The red dot and arrow represent the trip back to Timeline Zero.
Now a slightly more involved trip ... another team goes to 2014 to visit Morag and Vormir. Rhodes takes the power stone and returns. Nebula is captured by Thanos. Black Widow sacrifices herself so that Hawkeye can return with the Soul Stone. Thanos at a slightly later time figures out how to use the Pym Particles to arrive in Timeline Zero to stop the Avengers. We'll call this branch Timeline Thanos-2014.
The updated map:
The green dot and line represent the return of our Avengers (minus Black Widow) to 2023, and the purple dot and line represent Thanos' trip to Timeline Zero. We have no idea how long Thanos took to prepare for the trip ... a year? a week? But we do know that his ship arrived later that day in 2023.
Now the confusing one: A team goes back to New York in 2012, and whoa Nellie! Captain America secures the mind stone after fighting with himself -- definite evidence that we're dealing with a Many-Worlds model. Professor Hulk secures the time stone after listening to the Ancient One's nonsense about time travel. He also promises to return all the stones to their original places. Ant-man and Stark try to get the Tesseract, but fail miserably. Loki escapes amid all the commotion. Uh oh! We'll call this Timeline New-York-2012.
Stark and the Cap decide to go back to Indiana to get the Tesseract and more Pym juice. They end up in 1970. Stark grabs the Tesseract, runs into his father, while the Cap gets the Pym juice and sees his old girlfriend Carter through the window. We'll call this Timeline Indiana-1970.
Then Stark and the Cap return back to Timeline Zero.
Here's the new map:
The red dot from 2012 represents the Avengers who went straight back to 2023, while the brown dots and lines represent Stark and Cap's trip to 1970 and back to 2023.
Okay ... so far so good? Right now we have five total timelines. With everyone from all timelines returned back to 2023 in Timeline Zero, the big battle ensues. Thanos dies. Stark dies. Everyone cries.
At the end of the movie, the Cap volunteers to go back and return all the stones. However, there's one small problem. If the rules say that you can only travel backwards along the current timeline you're in now, how could the Cap ever return to those other 4 branch-off timelines? This is where I've seen many articles say that the Captain time travel bit broke everything.
But not so fast!
My work friend came up with the perfect answer. The Infinity Stones, themselves, want to return back to their respective timelines. So, as the Cap enters the quantum world, the stones would tether him back to the correct timelines.
As the Cap explains, he delivers the Time Stones first. Each jump requires a Pym juice bottle, but now with Mr. Pym back, we can assume that the Cap has sufficient vials for all the trips. He can deliver the Stones in any order he wishes, but for the sake of my picture, I'm going to say he travels to these in reverse order.
He hits Timeline Thanos-2014 to return the Soul Stone (wonder how that goes?), and the Power Stone. Then he goes to Timeline Thor-2013 to return the Ether (does he have it injected back into Jane?) and most likely also returns Mjölnir. Next comes Timeline New-York-2012 to return the Mind Stone (minus staff? -- he didn't bring that back) and the Time Stone. And finally, Timeline Indiana-1970 to return the Tesseract (how does he get it back to cubie form?).
From there, he can travel backward in time, following Timeline Indiana-1970 to the end of its branch and continuing on down Timeline Zero until he hits 1940's, starting a new timeline. We'll call this Timeline Carter-1940's.
After living a full life with his girlfriend, he decides to go back and give his shield to the Falcon. Since he's stuck in Timeline Carter-1940's, he can't naturally show up in Timeline Zero. He must do one more time jump. I think he could have used the earlier big platform as a tether to return -- perhaps in the few seconds before the original team comes back. And then he could have waited around to show up at the right moment to surprise everyone. As long as he stayed out of the way until then, it might not create another branch.
The Russo brothers give a possibly cleaner explanation: the Cap does return a few seconds after he left, but the Hulk's mess-ups cause him to show up over at the bench. I like that this avoids problems with possibly causing another branch, but I don't like that the Cap misses the platform. But perhaps overall, the Russo brothers' explanation is cleaner.
Either way, here's the final map, showing the Cap's travels in blue ...
We end up with six distinct timelines. Now that we've mapped everything out, we can finish with a closer look at each of the timeline to get a better understanding of what happens overall.
Timeline Zero: All the movies happen as the stories were told. The original Gamora is dead, but the new one remains in her place. Stark is dead. Black Widow is dead. Captain America is in retirement.
Timeline Carter-1940's: As long as the Cap stays out of the way, this timeline is going to resemble Timeline Zero closely. Perhaps the Cap is Carter's secret husband. In 2012, the frozen Cap will be unthawed, and events would unfold as expected ... except ... Zero Timeline Cap has stolen the shield and given it to the Falcon, leaving no shield for Frozen Cap later on. Though my son suggests that the Cap could have had a 2nd one created for Frozen Cap. Minor detail?
Timeline Indiana-1970's: Not much happened to change things, so events would probably play out the same as Timeline Zero. (Even possibly creating more copies of the time map above. Timelineception!!)
Timeline New-York-2012: This is the most interesting "messed-up" timeline. Loki has escaped. The Hydra folks are alerted to the fact that others know who they are. These loose threads were not closed. With Loki on the loose, it's impossible to predict how this timeline will differ from Timeline Zero. Rumors are that the announced Loki TV show may happen in this new universe. If so, we'll have to wait till then to get more answers.
Timeline Thor-2013: Not much changed here, either. Younger Thor probably wondered where Mjölnir went for a few minutes, and his mother probably died a little happier. Perhaps the whole Jane/Ether fiasco would cause some further scrutiny into the Reality Stone, which could cause things to play out differently. But on the most part, things should return to resembling Timeline Zero.
Timeline Thanos-2014: This timeline is definitely changed, most likely for the better. Thanos left this universe and died. No Thanos means no Infinity Wars, so whatever happens next in this universe, we might as well call it the Happy Path timeline. In fact, that timeline's Black Widow is still alive on Earth, and will never have to go back to sacrifice herself.
But it does raise the question: why did Thanos think it was worth going to the Zero Timeline where he had already won and fulfilled destiny? Without a tether, he could never return to his own timeline, and that universe would miss out on his destiny. A smarter Thanos would stay. A more hot-headed Thanos would do the stupid thing of going to another universe only to die in the process.
And before we end, here's one more bonus thing to think about. Remember when Doctor Strange found 14,000,605 possible futures? In the Many-Worlds model, all of these possible futures would have to exist in each of their own branches. But in seeing the One where they won, he saw it was necessary to give up the Time Stone. In doing so, he changed the probability distribution of winning among all the possible futures from that point. Those 14,000,605 universes would still exist, but with much less density, while the One future's probability increased. That's still a lot of universes that are going to be sad, and their stories will never be told.
And there you have it. Now that your mind's blown, and the timelines have been explained, you can now impress your friends with your grasp of all the timelines.