This is difficult to determine before a diagnosis has been made, as it depends to a large degree on your history, the kind of problems you are experiencing and how recently or how long ago the started.

However, it is useful to know that the effect of acupuncture is cumulative which is why a series of weekly sessions is usually the way to begin. 

If a problem has been with you a long time then it will probably take you a little longer to get well.   Sometimes though, even  a couple of sessions is enough to help reduce a particular problem.  Acupuncture is a fine form of preventative medicine and therefore many people opt, once well, to return for maintenance treatments perhaps every month or 6 weeks, or even just 4 or 5 times a year at the change of the seasons.