To directly answer you question of "how long does it take" is there isn't a good definitive answer.  Everyone is unique and it depends largely on your practice routine and determination.

I don't recall now how long it took me to be able to play all of the open chords.  I can change most of them smoothly but there are still a couple that trip me up.  But I'm much better now than when I started and you are too!

Keep practicing and keep reaching out when you get stuck!