Both, if the person has great potential. People with an aptitude for chess learn it in leaps and bounds, while others never get it. On the other hand, there is so much strategy and theory to learn that it takes at least two years to get past the basics.
But chess is rarely learned over night, even Bobby Fischer took a year or so before he "got good". To me, the last prodigy was Sammy Reshevsky.
And I also believe practice as well as reading about theory come hand in hand to improve. You need both to improve.
I love chess! If I could spend all day playing chess I would do so happily. My question is, do people become great chess players over night, or do you generally agree, that most just get better over time, and with a lot of practice?