The seminal text here is Lily Ross Taylor's The Voting Districts of the Roman Republic. It's been amended and added to over the years, but it's still the standard treatment of the tribal divisions.

The Romans knew that the tribes had been added to over time, and there was an official order of tribes that indicated their age as well as the order in which the lustrum proceeded through them. LRT identifies two basic phases of tribal creation. The oldest fifteen rural tribes were at least supposedly geographically based, representing fifteen of the major landholding clans of the ager Romanus. However, there's a bit of suspect evidence here, since LRT's reconstruction of the earliest tribes places them in a counterclockwise arrangement around the city, matching the counterclockwise procession of the lustrum through their territory (the same thing is mirrored in the four urban tribes). It's a bit hard to believe that these clans possessed territory in such a neat arrangement, so probably from the earliest period the tribal designations were approximate.

Up to 241, fourteen additional rural tribes were added as Roman power extended out past the ager Romanus. LRT supposes that most of these tribes were founded either by Roman colonists or by the enfranchisement of Italian tribal peoples. In either case, these tribes at least at first appear to form contiguous geographical belts, of varying size. The "martial" tribal peoples of the Apennines and eastern central Italy, such as the Marsi, were instrumental in the power of the Roman army, and together with the fortified military colonies provided a continuous militarized frontier that constrained other Italian peoples (often surrounding them), including nominal Roman allies, as well as insulating the ager Romanus from the near-constant warfare of the frontier. LRT supposes that these tribal designations were of a dual nature. Citizen colonies, of course, were founded with tribal designations from the very start, but in addition to this LRT supposes that the surrounding tribal peoples were, when they were granted citizenship, given individual viritane grants rather than being absorbed as citivates. Many of these peoples seem not to have had any walled towns, meaning that the colonies that both reinforced and policed them would have been the centers of citizen political activity.

By the end of the third century, the Romans were no longer establishing new tribes. Instead, as Roman citizenship spread through municipal grants to allied towns and the establishment of more and more colonial land distributions along the ever-expanding frontier, tribes were simply extended, often in weird patterns so that they didn't overlap. The tribal divisions of central Italy were, by the second century, extremely cramped, partly because of how old those divisions were but also because the extremely high urbanization of central Italy meant that there was a lot of population that had to be split up. Because of the geographic arrangement of the tribes, many of them couldn't be extended. Many of the oldest tribes, meanwhile, had extended in weird patterns as citizenship was extended to central Italian peoples adjacent to the oldest tribal areas. Some tribes basically only exist on the old ager Romanus and the surrounding area. The Tromentine tribe basically exists only at Veii, and then was extended to Fabrateria Nova when a Gracchan colony was founded there, randomly on the opposite side of central Italy. Other tribes were extended in a general direction as space allowed, creating kind of snakey boundaries between tribes. For example, the Voturian tribe extended along the west coast down to Antium but also north towards Caere. Sometimes land distributions of captured territory, a typical feature of the middle Republic, were all included in the same tribe, such as the distribution of Flaminius in 232 which divided both new and old citizens alike in the distributed area into the Pollian and Voturian tribes, resulting in a rather huge expansion of those tribes' areas.

In general, LRT suggests, during this period the tribes expanded in a basically directional pattern, jumping to the nearest free area in their general allotted direction when they were unable to expand contiguously (which was often). LRT supposes that this probably reflected the sections of the Campus Martius where the tribal contingents were drawn up during the levy, but that seems kind of conjectural to me. In any case, by the end of the second century tribal divisions were taking larger and larger chunks of Italian territory, and only a relative few tribes were taking up most of that land. As the Roman frontier expanded, particularly into Gaul in the north, the fortification of the frontier there created a fairly dense region of urbanization in Gaul and northern Italy. Whereas some tribes, like the Romilian tribe, were basically restricted to Campania and the territory that had been seized from old Roman enemies there, the frontier in the north continued to be active, providing constant new land that needed to be fortified and distributed. So the tribes in that direction--the Falernan, the Quirine, etc.--expanded greatly, chief among them the Pollian tribe, to which a huge amount of Gaul and Liguria was assigned. By this time the tribes had stopped being anything but voting districts, and while there's some evidence that tribal divisions were a conscious part of the identities of the elite and the people even into the post-Augustan period, for all practical purposes these were just voting districts.

The big change in the membership of the tribes must have been after 90, when the newly enfranchised Italians had to be distributed into the tribes. That program was much delayed, because there was initially some controversy over whether the Italians should be distributed into the existing tribes, or whether new tribes should be made for them. Our sources represent this debate as an attempt on the part of the old citizens to restrict the very numerous Italian population to only a few tribes, limiting their voting power, but at the same time we can also conjecture that some amount of precedent was probably at play here. After all, when new tribal peoples had been enfranchised they mostly had received their own tribal designations, or had been distributed according to geographical reasoning. So why shouldn't the new citizens be distributed in the same way? In the end, the new citizens were divided fairly evenly. The massive Pollian tribe received no additions, and the large tribes on the frontier were only increased where newly admitted municipia were contiguous to their territory, while the older tribes received allotments in what often seems at first glance to be random fashion. Many of these tribal allotments were not contiguous, and often new municipia were assigned to old tribes that had been hemmed in and were quite small. At the same time, the original tribal areas immediately around the city were probably dissolved and reorganized.

In short, by 90 all of Italy was distributed among the tribes, and the very few (short-lived) overseas colonies of the Republic were likewise given tribal assignments. Apart from some areas, like Gaul, where large sections of colonial and militarized land had been assigned to only a few tribes, the tribal map of Italy was something of a mess in the first century, and was so complicated that Q. Cicero recommends that political hopefuls memorize which towns belonged to which tribe in extensive detail, a time-consuming process that nevertheless would have helped an electoral candidate understand which areas to focus his attention on. It's no great surprise, then, that the municipalities of Gaul attracted so much campaigning attention after 70 (when the assignment of the Italians was completed), and seem to have been able to swing some elections!

Membership in the tribes remained, through the imperial period, nominally geographic. But in reality it was partially hereditary as well. Tribal membership was assigned by the censors during the census every five years, based on a citizen's primary residence. That causes problems, for a number of reasons. Most obviously, the census was extremely irregular in the first century, as successive censors either could not be elected or never completed their assignment. Through the 60s and 50s there were undoubtedly a lot of people who had moved around in Italy or had been displaced by the various crises that shook the region and who were never reassigned to their new tribes. Additionally, the criteria for tribal membership were not always the clearest. Most senators, for example, lived in Rome but belonged to rural tribes by virtue of their extra-urban landholdings. Similarly, a large portion of Rome's population was sort of semi-itinerant, probably nominally living in places like Umbria and Etruria but working as seasonal labor for long periods of time in Rome and other urban centers. On top of that, freedpeople were automatically assigned to one of the urban tribes, even though undoubtedly the larger portion of them lived in Italy or even the provinces. Citizens who had been assigned colonial plots appear to have maintained their assigned tribal identities even if they moved, and of course colonial foundations and land distributions changed one's tribe. By the imperial period tribal designations still appear sometimes on inscriptions, but usually as a way of indicating citizenship. By that period, trying to figure out why someone is part of one tribe rather than another is often pretty much impossible.