How towns are founded depends on when and where they started. Many communities in the US were neighborhoods or small villages, and then when enough people were there to need a post office, the USPS named the post office, which became the town name. Then city limits, governance, and services grew up around the community as needed. But today, the process is way more formalized. It's almost impossible to start a new town outside the US, and within the US, it depends greatly on which state laws govern the land. Half as Interesting explains how those laws vary.
But why in the world would you want to start a town? Towns are still subject to state and federal laws, and if you want to establish city services (utilities, policing, schools, etc.), you have to tax people and raise money to get those projects off the ground. It's much easier to just join an already-established town nearby instead of starting from scratch, as they can just expand their existing services instead. This video is not as long as you'd think, because the last two minutes are an ad.