To me it started to get fast when I got my self a good cube and started to learn fingertricks. That's when sub 1min happened.
My first sub20 second solve was after 7 months of practice, but I didn't practice that often.
I know someone who learned to solve in under a minute in 1 month. I've been cubing for about 2 months, and I still can't get it under a minute. It just takes onger for some people.
Well, it's hard to measure the time it takes. I personally would prefer something like the number of cubes you solved, for example: After about 200 solves I average sub 1-minute. That would make things much more comparable.
Since I know, that a Rubik's cube can be solves by an ordinary human (I didn't know^^) I immediately started cubing and got faster.
Now I've been cubing for about 4 weeks (single: 43 sec.), I think that's pretty fast... But I spend a lot of time with the cube and learn a lot of allgs.
It's different for all people so it isn't that useful to ask. Some who have been cubing for 2 years still average 30 seconds, or maybe more - just go with your style and you'll learn at the pace that is right for you
I reached sub-minute pretty easily but had to work hard for further improvement. The key is to get a lubricated cube and also to not push yourself. Remember, there are more important things in life other that cubing: eating, sleeping, and um, not much else
After a week, I was around 1:30. Two weeks and I was sub minute.
Hovered there for a long time, as I wasn't that in to it. I did maybe one solve a day, if that. Then I got really in to it, picked up Fridrich. So now it's been around a year, and I am at about 35.