That leaves your question at - how did the individual states, of the USA, come to terms with each other? Some thing like the home stead act may have an effect.
It was pretty much as you say: the Federal government frequently decided these things in a general or specific sense, especially as the larger original territories were organized into smaller territorial stretches that would become states, and the state would confirm these borders in its constitution when it applied for statehood. Certain fundamental territorial divisions frequently followed local rivers - the Mississippi, the Ohio, the Missouri, the Colorado, the Columbia, the Red. Many others were arbitrary flat lines; east of the Mississippi, many of these were rooted in pre-Independence colonial charters from lands ceded by the original colonies to federal organization, to wit Tennessee (North Carolina), Kentucky (Virginia), Alabama and Mississippi (Georgia). Others were flat lines rooted in geography - they were drawn from some geographic feature off in a direction until they hit something else, such as the border between Ohio and Michigan (which was actually, interestingly, drawn from a landmark in Indiana that wasn't followed for the border with Indiana, hence why the Indiana-Michigan and Ohio-Michigan borders don't match up). Others were drawn by latitude, especially in the Great American Desert (as it was termed then) where there were few major river confluences and major lakes to choose from - Kansas, Wyoming, Colorado, and so forth.
Interestingly, due to the fact that Congress frequently had to organize territories before detailed surveys of the land could be made, this could result in odd quirks. The northernmost border of Minnesota with Canada had the weird quirk that we today know as the Angle (which can only be reached overland by crossing Canada) due to the fact that people assumed the source of the Mississippi to be further north than it actually was, and the Michigan-Ohio border was supposed to go from the southernmost extent of Lake Michigan eastward until it reached Lake Erie (the dispute over how this line was to be drawn, thanks to Ohio defining it subtly differently from the original Federal wording, became the brief, poorly-named Toledo War that was won by everyone except Wisconsin). Similarly, the Honey War between Missouri and Iowa was "fought" (insofar as anyone can use that word for a bloodless conflict that included militias equipped with blunderbusses, flintlocks, and a sausage stuffer) over a lexical ambiguity in precisely which rapids the straight line of the border between the two states was to be drawn from. The Kentucky-Tennessee border is yet another such example of geographic snafus, which is why there's a "divot" in Tennessee west of the Tennessee river. This wasn't immune to popular appeal, either: just across the river, also, the Missouri-Arkansas border was supposed to follow the exact same latitude line, but gained its "boot" when the locals protested to Congress about being transferred to Arkansas. Every single time, it had to be arbitrated by the federal government in the end.
