From reading on legends Vader wasn’t taught much regarding the dark side but it seems in the new canon Sidious taught him the teachings of the sith, rituals, and made him go through trials fighting the remaining Jedi, getting a new saber.
Palpatine taught Vader the history and ways of the Sith, the uses of the dark side, the power gleaned from hatred and rage, as well as tactics and strategy.
Granted, Palpatine didn't regularly sit down with Vader for Sith tutoring sessions where he wrote on the chalkboard and Vader brought him an apple every morning -- rather he taught through object lessons and experience(this was the reason why Palpatine went on a mission with Vader in Lords of the Sith, and also why he sent Vader on missions with Tarkin and Thrawn in the Tarkin and Thrawn: Alliances novels respectively.)
Vader's daunting tasks of hunting down surviving Jedi, supervising the Inquisitorius, supporting the Imperial military, etc. etc... These were all lessons. This could also be the reason why Leia wasn't surprised to find someone "holding Vader's leash" during ANH -- at the time, he wasn't [yet] well-known for operating independently as a commander in the Imperial military. /shrug
That said, one of Palpatine's primary end-goals was to one day work together with Vader to unlock the ancient secrets of the Sith:
So he undoubtedly planned on using Vader to help carry out some of his 'broader' dark side machinations... But unfortunately, they likely never got the opportunity to do so, as Vader had to incessantly deal with the growing Rebel threat.
"The Grand Admiral was smart and subtle, but never used his brilliance to show up or humiliate anyone.
He demanded results, but never perfection, and had amazing stores of patience for those who were truly working to their fullest ability.
It was a pity Thrawn's style of leadership hadn't spread through the rest of the navy.
If that happened, he suspected, the Empire would stand forever."
Last edited by Galan007 on Aug 12th, 2018 at 10:01 PM