Yes, though they were not always followed to the letter. The Northwest Ordinance and Southwest Ordinance laid out the general plan for how white Americans envisioned their program of genocide and colonization. It began, of course, with white Americans contracting with some other white power to transfer ownership of land that as a practical matter neither polity controlled much of and without the people living there, usually regardless of whether white Americans understood them as also white, having any say in it at all. Texas and California are notable exceptions here, and also in other ways.

Making a tract of land legally part of the US came with the assumption that eventually the people actually living there who were not white, a thing white Americans simply could not forgive, would somehow "go away." That is, they'd be pushed off somewhere that white Americans did not want at that particular moment, for an indeterminate place further west where it was generally hoped that they would die out in short order. Those who didn't hope for indigenous Americans to die out generally saw their future involving the complete eradication of indigenous culture and its replacement with something suitably white and Protestant. This was all justified, when whites felt it required any justification, by the notion that indigenous and white Americans must naturally come to blows or otherwise harm each other by close proximity...which is completely ignoring how murderously vicious white Americans could routinely be on their frontier.

So step one is to acquire the land, in the eyes of white law. This land is then full of indigenous Americans, who have been there from time immemorial or since they were last forcibly dispossessed. Absent other legislation, this land then becomes formally unorganized territory. It has no form of government save direct federal oversight. It is also not open to white settlement, except in the form of employees of the United States in the persons of military personnel and Indian Agents. If a white person can't answer to one of those descriptions, they're fairly completely barred from even being present in what was often called simply Indian Country. (Major exceptions include missionaries and people moving along an established trail for white migration.) One could not establish a farm there, graze one's livestock, go hunting, or much of anything. All legal economic activity between civilians and Native Americans was to be done through the aforementioned agents, per a series of Non-Intercourse Acts. Obviously there's no force around competent to enforce that across the entirety of the white American frontier and corruption was a common thing among the agents to various First Nations -one of whom used his post to illegally import north of 100 enslaved people and set a Creek man up as the fall guy for it- but the system was imagined as one involving very little interaction.

Land could remain unorganized indefinitely, but the idea was that eventually whites would take it all. Until then Indigenous Americans were to be left alone, at least in theory. When white people decided they want to move in, they'd at least occasionally be cheeky enough to just cross the line and start up a town. (This happened in both Kansas and Nebraska, for example.) Said town might then elect a territorial delegate, send them to Washington, and demand they get a territorial government to make it all legal after the fact. This was sometimes done in reaction to the idea that Washington might be thinking that way regardless, but there's also a history of wildcat territorial governments demanding recognition and, later, even statehood.

Organizing a territorial government by the proper procedure, in the eyes of white legislators, involved an organic act from the federal government. Said act would organize -hence the name- a territory. That involved defining its bounds -often a bit larger than the state which we'd recognize with the same name and sometimes fantastically larger- and writing a basic law for it establishing how the territorial government would function, what powers it would have, and so on. For Kansas and Nebraska, each was given an assembly (lower house) and council (upper). Those were usually elected by the white men on the ground, but the territorial executive was appointed in Washington. Washington also retained veto power over any law the territory voted through...and footed the bill for the lot of this.

At this point the territory is opened for white settlement. What it is not is surveyed or comprehensively governed. The result is usually quite a lot of fighting about who owns what land and what constitutes a claim one is bound to respect. You also get stuff like people mistakenly or purposefully setting themselves up inside military or Indian reservations and hoping to flip that land or just keep it for themselves. White colonists will make claims by nailing cards to trees, putting up sticks, and throw together at what they think are good places for towns to organize companies that monopolize that land and get to sell it at a tidy profit down the way. There are various customs governing how this ought to work, squatter law, but the real measure is mostly what you can convince or intimidate your neighbors into backing. Usually there's a preference for people actually present, since whites from back east can and do hire agents to go out and pick up land for them as an investment.

All of this can be going on before the governor and the rest of the government even arrives, but once he does the governor has vast power. Until he chooses to run a census and conduct elections, he essentially runs the joint. In especially contentious situations, like Kansas', those decisions can be extremely sensitive. But that's not meant to go on for very long and eventually a territorial government would be voted in. A typical one is going to be very heavy on people from the state immediately to the east, who may or may not live in the territory on a regular basis. They'll generally adopt the laws of that same state as a place to get started and go about the usual business of running the territory.

Preparatory to organization and often continuing through all this, Washington will send out or appoint a local agent to negotiate with Native Americans about how their reservations will be reduced and/or relocated. That could be foisted on the same people multiple times in a few decades. Of course when statehood comes, the state government can claim it has no legal obligations to any First Nation and those reservation boundaries may get another unwelcome round of reductions.

There's no set point for when the territorial phase ends. White Americans under a territorial government consider themselves in a colonial situation that is meant to be temporary, but it's 100% up to Washington when they get to advance to statehood. The idea of the territorial stage, at which time they are sometimes described as inchoate states, is that they'll use it to get their house in order and then will ask leave to write a constitution. This would be given by Washington in the form of an enabling act, through which the nation may place constraints on what can be in the state constitution in order for it to be acceptable. Until 1854, it was accepted practice that some of these acts would come with riders prohibiting enslaving people...though new states can and did get around that one by instituting forms of slavery lacking only the name right after statehood -Illinois and Indiana are big culprits- and there were attempts to just do it outright; the vote in Illinois was very close. There's usually also some specification of the new state's boundaries, at which point Territory X tends to assume the shape we'd recognize as X on the map...but there are a few exceptions.

Assuming the territory doesn't devolve into a small civil war (Kansas) and/or become a pawn for larger disputes (Kansas, Maine and Missouri are conspicuous here) and its boundaries are settled well enough for Washington's liking -Michigan's statehood was delayed in part due its neighbors helping themselves to land legally allocated to Michigan Territory, for which it was compensated with the majority of the Upper Peninsula...which was at Wisconsin's expense- the done thing would be for it to write up that constitution and submit it for Washington's consideration. Most of the time, that's not a big issue. When it is, usually slavery is involved. As a matter of law, Washington can delay statehood in perpetuity. In practice, this is often hard to achieve. When the history of the matter came up related to Kansas the House put together a committee to look into things and they reported that the Congress had previously accepted wildcat governments and wildcat constitutions as suitable for admission to the Union, complete with examples. Washington was generally not bloody-minded about forcing a territory into statehood, but seeing statehood as a natural progression by which a white man would regain his full rights as an American citizen made it very hard for the white men in Washington to refuse what seemed to be committed candidates working on their own initiative. Either way, your end product is a new state for white Americans and continued deprivation for everyone else.