Everyone on the crew had to train their abilities to get to where they are, even before the timeskip.
Luffy: Trained as a child with Ace and Sabo.
Zoro: Trained at Koshiro's dojo, then left and trained on his own.
Nami: Trained after her battle against Miss Doublefinger showed her she could've been killed and she needed to get better. This was proven when she mastered her abilities in Enies Lobby.
Usopp: Trained his accuracy since he was a child, even through it seems to be hereditary.
Sanji: Trained under Zeff since they returned from the deserted island and opened the Baratie.
Chopper: Trained under Kureha, where he created the Rumble Balls.
Robin: Trained and mastered her abilities, since she needed to do so to survive, while she was on the run those 20 years.
Franky: Trained and re-built himself after faking his death.
Brook: Didn't really need to, but my bet is that he practiced a bit while stranded on the Florian Triangle.