I understand the history and procedure for homesteading and the land acts that went with that but I don't understand how towns were actually created from the land. Say Smithtown was founded on a creek by John Smith in 1870. Did John Smith buy the land around the creek, plat it, and sell the individual lots or did the government decided his plan was good and platted the land and sold it themselves? How were the individual parcels of land obtained and sold in old towns?
Many Americans seem to know about the Homestead Act but they generally don't realize that the giving of land in the homestead act was just a small part of distributing Federal Lands. After the American Revolution the Federal Government had control of a huge area of land called The Northwest Territory. Then they acquired even more land with the Louisiana Purchase Then there was the Mexican American War and various land purchases and pretty soon the Government of the United States of America owned a huge chunk of earth. They immediately set about selling this land.
In 1796 a law was established for sale of these lands. This law divided the land up into 640 acre parcels and sold the parcels at auction. The minimum price was set at $2/acre at that time but it was gradually reduced over the next 60 years. $1280 dollars was more than one person could generally come up with and 640 acres was more than a single farmer could farm at that time so groups of people got together and would purchase the lands as a group to make a town. Often the town would be named after the leader of this group so if John Smith organized the settlers for the town the town might come to be named Smithtown.
It also wasn't uncommon for land speculators to buy a plot for a town and then sell individual parcels from that land. You have to remember that Towns require many things to make them successful. (I'm going to give a shoutout to SimCity here because they actually got some things right) If there is no road going to your Town it isn't going to last long. If there isn't a store or a blacksmith shop or any places to work the town just isn't going to survive. The developers who planned these towns built roads and shops and all the necessities of a town and then made their profit from selling plots of land within the town. In these cases the developer could name their town anything they wanted to.
Places that already had infrastructure in place or that were just more desirable in general usually fetched a higher price at auction. For example a plot right next to a road and a ferry would cost more than a plot located on a rocky plot of land in the middle of a swamp.
Over time the lot sizes fell from 640 acres to a low of just 80 acres. The price dropped from $2/acre to $1/acre until finally the federal government began just giving away land through acts such as the homestead act and the land grant act.
Occasionally land would be sold in smaller parcels due to unusual circumstances for example a town might spring up around a fort built on a major road. In these cases smaller parcels of land within the town would be auctioned by the government.
I mentioned the Land Grant Act earlier. This gave some Federal Lands to the States so they could sell the lands, sale of these lands were the original funding for Land Grant Colleges. Distribution of these lands was usually done by the states in a similar manner to the Federal Government.
The short answer to your question would be that the land was usually sold at public auction. Most homesteads couldn't become towns because if you couldn't afford to buy land you probably couldn't afford to build the infrastructure that towns need to thrive.