I'm more familiar with the colonization process of SAI because it was pretty recent for my chapter (1999) and not so current on the Phi Sig policies.
In SAI, you first must form an interest group of at least 15 non-graduating girls of sophomore status or higher. The group must form themselves and become a free standing organization that volunteers in the community, hosts events, raises funds, etc. The interest group has to submit letters from the President of the University and the Head of the Music Department in support of Sigma Alpha Iota. An official pre-colonization visit must be held with school officials, group member and an official Sigma Alpha Iota representative.
Once the group is approved to colony status they must meet certain goals which include weekly meetings, minutes of each meeting, service projects, fund raisers, elect officers, establish a bank account...etc, etc. The colony must show evidence of operating for 6 months post the pre-colonization meeting.
A post-petition meeting is held with another representative who must observe certain things, meet with certain important people and report back to the NEB with their recommendation to approve/not approve the group for colony status. If the group is approved, the NVP or other rep will perform the pledging ceremony for the colony members and they will begin the Member in Training period.
The Province Officer, Faculty advisor, or other appointed Fraternity member will conduct the Member in Training sessions for the duration of 6 to 10 weeks. At the end of the MiT period, the colony members must take and pass the national membership exam.
At the end of it all, the colony is installed as a chapter and then initiated over a weekend--the whole thing usually takes 1 and 1/2 days. The installation day must include a reception and musicale.
Sorry....I talk too much.
ETA: I'm gonna look up the Phi Sig process now.