The President of the chapter should have all of the information you need regarding affiliation - and the Chapter Advisor, too. There are some forms that you have to fill out and have someone from your initiating chapter fill out. The chapter does have to vote for the affiliation to go through. Once approved, you are a regular member of their chapter - no 8-week period involved. You become a fully functioning collegiate member of their chapter. Again, it's all spelled out in their handbooks.
Good luck to you!