In the Disney Canon, Luke's lightsaber training takes place in a series of events, spanning from his first lesson with Obi-wan Kenobi, to the completion of his training with Master Yoda, and on from there. His lightsaber training also took place alongside his general Force training over this time, and occurred in the context of already being very naturally talented.
From the three movies (ANH, TESB and ROTJ), as well as The Weapon of a Jedi: A Luke Skywalker Adventure, Heir to the Jedi, Star Wars 2: Skywalker Strikes, Part II, and Star Wars Book I: Skywalker Strikes, amongst other sources, the general path seems to be:
A brief training session with Obi-wan Kenobi and a training remote onboard the Millenium Falcon, on the way to Alderaan, where he learned the basics of lightsaber form
On Devaron he found training remotes and used his previous training from Kenobi to practice and improve against the exercises the went through
Luke returned to Tatooine and found The Journals of Ben Kenobi that Kenobi had written and left for him, and he proceeded to study there from there onwards, including information about lightsaber combat
On Nar Shaddaa, he was caught by Grakkus and trained by a figure called the gamemaster in lightsaber combat
He presumably underwent lightsaber training on Dagobah with Yoda, though it is not shown on-screen in TESB
Note that all of this takes place before his duel with Vader on Bespin
Beyond this, as ancillary to lightsaber training itself, he:
Practiced privately during this time
Learned about how to construct a lightsaber based on studying Huulik's lightsaber and any information given to him by Obi-wan Kenobi, culminating in his construction of his own/new lightsaber on Tatooine right before rescuing Han Solo from Jabba the Hutt
Over this time, Luke also grew stronger in the Force, and engaged in several duels/combats, which presumably increased his skill and experience, such as:
A ghest on Rodia
Bounty hunters on Omereth
Stormtroopers on Devaron
A brief duel with Darth Vader on Cymoon I
Boba Fett on Tatooine
Stormtroopers, and Kongo the Disemboweler, a beast with lightsaber-resistant armor, in the arena in Grakkus' Palace
A second duel on Bespin with Darth Vader (where Vader wasn't trying to kill him, only defeat, subdue and turn him to the dark side)
The rescue of Han Solo on Tatooine, and all that that entailed (including holding off Boba Fett, again)
His final duel with Darth Vader, where he managed to defeat him
Other SFF.se sources can be found here, here and here, wherein the nature of his training and his duels with Vader, amongst other things, is discussed.
N.B.1. Although it does not bear directly on the OP, during this period, his lightsaber form was Form V. Although it is not explicitly stated how or why he came to this form, its nature is suggestive. It is a form that is very effective against blasters and multiple opponents (useful against the Empire), takes advantage of the emotion/aggression and physical vigor of the user (both qualities Luke had at this point), and is the form that Luke would have observed Darth Vader using in his duels with him.
When compared to the other lightsaber forms, Form V may have been the most plausible for Skywalker to use since Form I was ineffective against other lightsabers, Form II required too much finesse and skill for a padawan, Form III was too defensive and again required a mastery of it to be truely effective (against highly competent opponents like Vader or the Emperor), Form IV wasn't good in tight spaces or prolonged combat (a problem for an inexperienced fighter who would not be able to defeat a skilled opponent quickly) or against blasters, Form VI required experience and passive control and force talents intermingled with it, and Form VII was too close to the dark side.
N.B.2. Although it exists outside of the current Disney Canon, after his duel with Vader, as Luke created the New Jedi Order, it is presumed that he learned more extensively about lightsaber combat from recovered holocrons and other more conventional sources.
