How exactly does time work in 'Avengers: Endgame'?

Warning: MAJOR spoilers for Avengers: Endgame below.Time travel can save the fate of the Marvel Cinematic Universe, and make your brain throb worse than a hammer to the head all at the same time!
Leading up to the epic release of Avengers: Endgame, plenty of folks (yours truly included) were worried that the inevitable addition of time travel to the MCU would undermine the series' fundamental structure and leave our favorite heroes in a pile of mind-numbing paradoxes, fallacies, and plot holes.