I can't think of any official background off the top of my head that covers the process in any detail, so it's an open field for you to explore.
To start with however, you would first need to decide how you define a 'Sept'. Some people, including a few GW writers, consider Septs as individual star-systems or even planets. Others however, including myself, instead see them as large semi-autonomous territories covering multiple star-systems and celestial features within a region of space, similar to Soviet SSRs or US states but on an interstellar scale.
Which version you go with will influence the exact specifics, but either way it's a very long process. Any Spet outside of T'au will have begun life as a colony. There are generally two classes of Tau colony worlds, First Phase colonies with a population larger than 100,000 inhabitants and considerable infrastructure and Second Phase colonies with a population of between 10 and 10,000 individuals and more limited settlement (often little more than a few automated mining stations/refineries/farm complexes/other resource producing infrastructure, the few personnel required to oversee them and a Firewarrior garrison for security). These terms are not to be confused with the Spheres of Expansion, which are an independent categorisation.
In theory there is nothing stopping either class of colony from becoming a Sept, but First Phase colonies would generally have a better chance given their larger population and greater infrastructure development. Once a colony reaches a suitable level of population size and infrastructure development, and begins to take steps towards setting up colonies of its own, it can start to be considered as a potential new Sept (Knightofthewr's Fo'tan, first created for the Into Silence project, is a good example of a Tau territory at this state of development).
The second element of being a Sept is cultural development. Much like the aforementioned SSRs and states, each Sept generally has its own cultural identity, with a distinct set of important history and personal idiosyncrasies - Dal'yth is a cosmopolitan melting-pot, Kel'shan has a reputation for being suspicious of outsiders, Bork'an and Fal'shia are both considered scientific powerhouses and so on. It stands to reason that developing such a cultural identity would be an important factor in becoming a Sept.
Both of these elements, especially the second one, take a very long time to come to fruition - the rapid development of numerous Third Sphere Septs is likely an exception caused from extensive investment from prominent Septs (similar to the rapid buildup that led to Alaska becoming a state in the 1950s).