Luke Skywalker's extreme abilities have puzzled some fans for years. As Yoda points out in Empire Strikes Back (and as we see in the prequels), most Jedi are taken in at a very young age and trained for a decade or more before becoming a Jedi Knight. On top of all that, it takes many additional years and trials before earning the status of Jedi Master. Compare all this to Luke Skywalker, the guy who basically spent a long weekend with Obi-Wan and a month with Yoda. So how did the guy who would've failed Jedi Academy on his attendance record become such a powerful figure in the Star Wars universe?
For one thing, Luke has a natural leg up on many Jedi because he's the son of Vader. While people scoff at midi-chlorians, these microscopic life forms were probably passed from father to son, explaining why Luke has inherited so much of Vader's raw power. He's also trained himself rather extensively. After all, he had to teach himself how to do cool tricks like summoning his lightsaber between A New Hope and Empire Strikes Back, and he clearly educated himself even more between Empire and Return of the Jedi, as he built his own lightsaber.
Plus, his instructors were also pretty amazing. Obi-Wan had experiences and knowledge that few Jedi ever had, and Yoda was in a league of his own in terms of powers, ability, and wisdom. A little bit of training with these guys is likely better than a decade with someone else, and once Obi-Wan started manifesting his Force ghost, it was clear he could continue to help train Luke. Finally, Luke looks amazing because he's fighting against non-Force users. And when he finally does face down with a Sith in Return of the Jedi, he isn't really trying to kill Vader. After all, it's his dear old dad.