The information we have about Darth Plagueis from canon is very limited and comes from only two sources: Episode III and the canon novel Tarkin.
The most relevant facts are that Plagueis was Sidious' master until some time after Sidious became the senator from Naboo:
[Sidious and Tarkin] had met several years after Sidious -- still an apprentice of Darth Plagueis at the time -- had been appointed Naboo’s representative to the Republic Senate.
Tarkin, p. 102
We don't know exactly when Plagueis was murdered -- he may or may not have been alive during the events of Episode I.
We also know that Plagueis disdained "trivial" political matters and did not foresee that Sidious would rise to become Emperor:
The Emperor spent a long moment studying Ison and Rancit, stretching out with his powers to discern alignments, configurations, some syzygy of events. Then his thoughts turned to Vader and Tarkin. He appreciated how well they were working together, but he began to wonder if they were perhaps too close to the details of the dissidents’ scheme to recognize their ultimate objective. One needed to have a safe remove, as he felt he had, gazing into the 3-D representation of the galaxy he had made his own. How Plagueis would have mocked him for allowing himself to become personally involved in such a seemingly trivial matter; but then his Master had never foreseen that his onetime apprentice would become Emperor.
p. 103
From these two pieces of information we can make an educated guess: Plagueis and Sidious apparently had a disagreement about how to proceed with their attack on the Jedi/Republic; this disagreement precipitated a conflict between them which Sidious won, but Sidious was unable to learn how to cheat death from Plagueis (assuming Plagueis had learned it) before the murder. Sidious probably decided that he needed to go his own way, so he killed Plagueis in surprise -- this would be consistent with Sidious' story to Anakin about Plagueis being killed in his sleep.
We do know from canon that Plagueis and Sidious apparently tried to learn the final secrets of the dark side of the Force (such as cheating death), but it's not clear if Plagueis ever figured it out:
Save for Sidious, no sentient being in close to five thousand years had set foot in the shrine [under the former Jedi Temple]. The room’s excavation and restoration had been carried out by machines under the supervision of 11-4D. Even Vader was unaware of the shrine’s existence. But it was here that they would one day work together the way Sidious and Plagueis had to coax from the dark side its final secrets. In the intervening years he had actually come to appreciate Plagueis for the planner and prophet he had been. Such perilous machinations required two Sith, one to serve as bait for the dark side, the other to be the vessel. Success would grant them the power to harness the full powers of the dark side, and allow them to rule for ten thousand years.
p. 101
Even though Sidious did not know how to cheat death, it was a superb way to tempt Anakin to the dark side.
Although you've asked for only canon sources, the Legends novel Darth Plagueis is worth mentioning since it provides a story of Plagueis' murder that is consistent with the canon information about Plagueis.
In the novel, Plagueis helped Sidious maneuver himself into position to be elected Supreme Chancellor of the Republic. Plagueis' plan was that Palpatine would appoint Hego Damask (Plagueis' public identity) co-chancellor and Plagueis would rule behind the scenes:
[Sidious:] "...my knowledge of the dark side will never equal yours. The title [of Supreme Chancellor], the crown, should be yours.”
[Plagueis:] “And it will be, once you openly appoint me co-chancellor. Feared and respected by the galaxy’s most powerful beings, Hego Damask will be seen as a windfall for the Republic. But even then I will advise only in secret from behind your throne.”
p. 188
Sidious, however, was too power-hungry to agree to that plan. When Sidious murdered Plagueis he revealed a long list of complaints against Plagueis, some of which hint at why Sidious chose to murder Plagueis before learning how to cheat death:
"...It was Hego Damask as Plagueis who then set his sights on a seemingly confused young man and, with meticulous skill, manipulated him into committing patricide, matricide, fratricide. Darth Plagueis who took him as an apprentice, sharing some of his knowledge but withholding his most powerful secrets, denying the apprentice his wishes as a means of controlling him, instilling in him a sense of murderous rage, and turning him to the dark side.”
...
“Plagueis, who turned away from the Grand Plan to focus entirely on himself, in an egotistical quest for immortality.
...
“Plagueis who attempted to turn his equally powerful apprentice into a messenger and mere intermediary.
...
Sidious paused, then, in derision, added, “Plagueis the Wise, who in his time truly was, except at the end, trusting that the Rule of Two had been superseded, and failed to realize that he would not be excused from it. Plagueis the Wise, who forged the most powerful Sith Lord the galaxy has ever known, and yet who forgot to leave a place for himself; whose pride never allowed him to question that he would no longer be needed.”
p. 356
Sidious felt that Plagueis was hiding secrets (like how to cheat death) from him and that Plagueis never planned to teach him, so there was no point in keeping Plagueis alive longer. Sidious also felt that Plagueis was no longer necessary for Sidious to enact his political plans and attack against the Jedi and Republic. Since Sidious felt that Plagueis was no longer necessary, Sidious decided to grab all the power for himself.
While not canon, this story is consistent with what we know about Plagueis and with Sidious' power-hungry character.
