McIrish-
I hate to say this but I think the answer is, "it depends." The factors one must consider, among other things are what "competent" means and if the person has played any form of poker previously.
I'm not an expert but here are my thoughts under the following parameters;
1)We are referring to a recreational player attempting to become "competent" not a professional player,
2)Competent - Defined as a winning player at a common low limit say 1/2 or 3/6,
3)The player is of average intelligence or better and wants to win,
4)The player has played some form (home type games) of poker previously on more than a handful of occasions,
5) The player is attempting to become "competent" at Texas Hold Em and has never played before, and
6) The player faces competition of average skill level.
Under those assumptions, I think it would take probably two years of playing fairly regularly (a few times a month) to get a good feel for the game and begin to win. If our "player" read a book or two, knows a bit about probablility/statistics, and played regularly, he could narrow that down to a year or so.