This is a pretty common question asked in this subreddit, and an understandable one when you see just how many issues there are.
What you need to know before reading on is there are many universes in the Marvel world, all featuring the same or new characters in different timelines. This is so we can have other stories run along-side each other, and we can also have one-off stories that will make no sense and/or interfere with other running issues. There are two recommended universes to beginners and they are-
Earth-616 is the name used for the primary continuity where most Marvel stories take place, it's where we saw Peter Parker was originally bit back in 1962. It's the home of The Amazing Spider-Man comics that we all think of first.
The Ultimate Universe is a modern re-telling of Marvel's world. It started in 2000 with Ultimate Spider-Man, and the success of it brought along Ultimate X-Men, Fantastic Four, and The Ultimates (Think The Avengers), as well as many other characters. The Ultimate universe is referred to as Earth-1610.
These two universes are completely separate stories, however, they have met and and crossed paths in the past. If you wish to read everything, from beginning to end of either Universe, you can find the complete reading order for Earth-616 here and Earth-1610 here
This section will contain some some spoilers I'll give so you know the last key thing prior to the issue, as well as everything in the build up to it. It's in chronological order, so if you find a starting point you like the sounds of then stop reading this there, as the next entry will contain spoilers!
Places to start with Earth-616-
Brand New Day Amazing Spider-Man #546.
The Demon Mephisto is Peter's only way of saving Aunt May, but Mephisto's terms of doing-so is that he wants Peter's and Mary Jane's marriage as his price. Peter and MJ agree to his terms on the condition that Spider-Man's identity is returned to a secret. MJ reassures Peter that their love has endured so much already that she is sure one day they'll fall back in love and return to each other. Everything goes black, and begins a Brand New Day.
Superior Spider-Man Superior Spider-Man #1
Otto Octavius is dying from a lifetime of fighting superheroes. In an effort to pro-long his life he uses his machine The Octobot to transfer consciousness between himself and Peter Parker. Now with his mind in Peter's body, he has access to his powers, and even his memories. Octavius, now in Peter's body, attempts to kill his old body and with it Peter, just before the final blow is struck, Octavius see's the memories of Peter, and with it see's why he became Spider-Man. He stops, and instead promises to keep the people safe as Peter finally dies. With the death of Peter Parker, Octavius promises that with his intelligence and ambition, he will be a Superior Spider-Man.
Amazing Again! Amazing Spider-Man #1 Vol.3
The Goblin King has captured Anna Maria, Otto's love, and Otto is unable to save her. Now in each other's minds, Peter and Otto are communicating with each other through memories. Otto comes to terms with the fact he was never the better Spider-Man. Otto erases his consciousness and gives Peter his body back, entrusting that he will be the one to save his love, Anna Maria, as he fades away. Peter then defeats the Goblin King and saves Anna Maria, but quickly comes to the conclusion that for Peter to be alive, someone had to die, with that person being Otto Octavius, the superior Spider-Man. Old friends become new enemies, and a transdimensional vampire is about to start a Spider cull.
Places to start with Earth-1610-
Powerless Ultimate Spider-Man #1
A brand new start on Peter's story. This is a re-imagining of Amazing Fantasy #15, Spider-Man's first apperance.
Ultimate Fallout Ultimate Fallout Chapter 1
Peter has taken a bullet from the Punisher, and soon runs into The Green Goblin, Electro, Sandman, and the Vulture where Peter manages to defeat them despite his wounds, in front of the whole world. Normon tries after Peter once more and in one last effort, Peter throws MJ to safety before crushing Normon with a truck, but Peter is unable to get out of the way before the truck explodes due to his wounds. Peter now flung away from the scene by the explosion, MJ rushes over to him where Peter Parker has just died in her arms.
Thanks to u/kiekan for the Earth-616 Chronology and for keeping it up to date!