I do not know about most people here but when I first learned to snowboard (with my school in grade 6) it took me a good 8 times out to finally be able to link my turns and make it down the whole hill without falling. Within the first 4 times I could toe-side turn but did not feel very comfortable on my heel-side. I think it took 6 times to link turns and be comfortable and 8 times before I could really start laying into the edge and feel like I wasn't going to fall (and to start to go fast). Once I was really comfortable I found the transition from simple linked turns to carving was pretty quick and straightforward. For me 8 times out=8 weeks (with the school program) and then the next year I went to Jay Peak and was comfortable enough going down the blacks at Jay, but I wouldn't have done that my first year.
But I might have been a slow learner, I know people that picked it up in about 3 weeks (3 times out). I was always a little scared to fall (it is soooo sudden when you catch an edge-absolutely nothing like falling on skis, which I don't care about). And I found people that took a more aggresive approach to learning tended to learn faster.
As a former ski and snowboard instructor I probably shouldn't say this BUT I don't think its that useful to go to a lesson as an absolute beginner, you really just need to get a feel for the board and boarding and your friends can give you tips. But that is really just my experience. I am sure other people will have different experiences. For me I found the lesson really helped when I was already able to link turns and the instructor was telling me how to board more aggresively.