It depends on the individual. Some pick it up faster than others. Check out the Remembering The Kanji Method and also search up "Anki" on google. Anki is very useful nowadays, it's a spaced repetition flashcard system. You'll learn in no time. I tend to learn vocabulary from context, and from that I learn new kanji and other kanji compounds it can appear in. To put it short, there is no set time! Some people say you can learn 2,040 kanji in six months, but I wouldn't say that they are learned well or have a solid foundation. It's just all about using the kanji you learn and reading it too. Good luck. :)

This is the same as asking "how long would it take me to learn all the words in the English language?"