The number of treatments vary from person to person, disease to disease and depend on a variety of factors: your constitution, the severity and duration of the problem and the quantity / quality of your Qi.
Some experience immediate relief while others take months or even years to achieve results. Chronic conditions usually take longer to resolve than acute ones.
Plan on a minimum of a month, given that you are getting treated once a week to see significant changes.
An Acupuncturist may suggest one or two treatments per week, monthly visits for health maintenance or seasonal tune ups.