1) Luke naturally took to the lightsaber and with only a few verbal cues from Obi-Wan was able to 'see' using the living Force.
2) Prior to his introduction into the 'larger world' of the Force, Luke was a whiny brat. The more he used the Force the less and less whiny he got. (again think PT Anakin here)
3) Luke, with no 'canon' evidence that Obi-Wan continued to 'train' him after the events of ANH, trained HIMSELF enough to not only seem wiser by the start of ESB but also to be able to use the Force to move objects (in the Wampa lair).
4) That said, Yoda- despite his reluctance at first to want to train Luke- already had a good starting point with what Luke had already learned on his own.
5) Again with no 'canon' evidence (discounting SOTE which I have forgotten what little I knew about it) to the contrary, it would *appear* Luke continued his own training after the events of ESB. By the start of ROTJ he was a bad-mamma-jamma and after the Jabba affair he went *back* to Yoda to 'complete his training' Yoda tells Luke "No more training do you require. Already know you that which you need." Again, IMHO, by watching the PT I somehow doubt Anakin could have done that.
So basically what I'm saying is that Luke was an aberration but in a good way. In fact I'd even go as far to say that he... raised in more ways than one as the son of a planet of two suns... may be (by actions and not by Lucas' words) the closest to a 'chosen one' that the SW series had to offer.
As for 'old school' Jedi training... good question. The horrific editing and pacing of the PT coupled with the lack of revelation to any of the 'behind-the-scenes' Jedi training gave no clue as to the time period of standard training. Perhaps the Jedi just sit around in a circle and muse about the Force until experience walks in and smacks them in the face.
