Assume that one has begun a PhD program at a university which allows a student to choose an advisor after his/her first year in the program and the student has narrowed down to a couple of potential advisors and has taken at least one course with each of them.
As soon as is reasonable.
Think of it this way. There are possibly other students competing to work with this advisor, and they might have funds only for one new student. There might be other considerations - maybe the advisor is going on sabbatical, or isn't taking new students, and so on.
So as soon as possible, set up a meeting with the potential advisor, indicate your potential interest (and why!), and ask them point blank if they're taking students, and how they prefer to screen students (some do it through course work, some might like to work with you on an independent study project, and so on).
Depending on what they say, you can take further followup action - maybe they want you to take their class, and maybe they have a research group that has open meetings, and so on.
Bottom line: don't wait till your year is over, because it is quite possible that someone has made a decision already.
Caveat: if this year-delay is institutionalized, it might be that all advisors wait till the end of the year to even think about new students. I suspect this is unlikely, but in any case that first meeting will help clarify it.
It is never too early to contact potential advisers. If you have your heart set on a particular individual, you may even want to initiate contact before you start (and perhaps as early as right after you have applied). Early contacts usually come from motivated students.
Waiting a while gives you the ability to get to know the adviser and helps them get to know you. This could be beneficial, but you should not wait too long. Last minute contacts suggest a variety of behaviors that are unappealing in a graduate student, like laziness, forgetfulness, lack of dedication, etc.
If the program lets graduate students choose, then the advisers are well aware of how the system works. A short email requesting more information and an in person interview would be appropriate. If you know the adviser better (you have already taken a class with this person), then an informal stop by their office would be fine, too. Most advisers expect this kind of contact in this situation. An initial contact by email does not have to be anything more than:
Dear Professor {X}, I am (or will be soon) a graduate student in your department. I am interested in joining your research group. I have read about your work in the field of {Y} and found it interesting, and I want to learn more. Are you available to meet with me at one of the following times {suggest three specific times}? Thanks.
