Nobody was ever confused about why Luke got better at things between films because it was very clear to the audience that time had passed. In movie #2 we open with a new status quo - these people are now established figures in the rebellion, the empire has found their new secret base, they give us hints of the off-screen relationship developing between Han and Leia, and Luke demonstrates new abilities. At the start of movie #3 time has passed again, people have tracked down Han after he was taken away, and Luke is explicitly introduced in a much more calm and confident manner - he's totally comfortable with his powers now in a way he wasn't in the last film. Where was he practicing? Did he find some books, or an off-screen teacher, or did he figure it out from first principles? We don't know, but we don't really have to know, that aspect of it isn't significant to the story.
Something worth emphasizing here is that Luke's development in terms of power is uncharacteristically restrained by the standards of action/adventure narratives. If you watch contemporaneous SciFi and Fantasy adventure films, the expected arc for Star Wars (episode 4) would be that Luke comes into his full powers as a Jedi Knight Chosen One type person in the final act, maybe gets visions of his father or something, and then he not only stops the evil plot, he would kill Darth Vader in a sword fight straight up. Star Wars holding back on doing this is one of the things that sets it apart, and one of the reasons why it was turned so successfully into a series of movies, rather than having everything wrapped up in one. It managed to feel satisfying while still leaving loose threads to explore in the future movies - Luke has only taken a step into his powers, Darth Vader didn't die, the mysterious Emperor has never been seen, and the Empire has only been thwarted, not defeated outright.
Rey coming into her powers much quicker and more spectacularly is more in line with how most movies would have done it. They still let the bad guy get away at the end, and they're definitely still keeping a firm eye towards this being part of a series as opposed to a standalone movie, but they really don't waste much time powering her up. The depictions of how the Force works are, imo, quite bad in the sequel trilogy, but this was just carrying that torch from the prequels, where we had many of the same problems. Not all of the same, but many. Annakin being a Chosen One makes him stand out from other Jedi, in that he doesn't seem to need hard work because he is Very Special (tm). A lot of people roll their eyes at how shitty the scenes of him blowing up the trade federation ships are, but I think that beyond the surface level stupidity of all those scenes is the implication that it all kinda works how Finn says it does in The Force Awakens. Basically, you can just wing it, everything will be fine, because The Force will take care of it. It's pretty obnoxious.