About 15 years ago I saw an independent film at a local theater and it turned out that the guy who made it was couch-surfing the country showing the film at small theaters and was staying that night with a friend of a friend, so after the showing we went over to the friend's place to hang out and talk.
The guy who made the film was pretty cool and told us lots about the process. Basically he spent a year and all his time and money on it, borrowed money from everyone he knew, and pulled favors from all his friends and their friends to get access to locations for shooting, costumes, props, etc.
What it came down to was that at that level there is no process. You just call in every favor you can, make lots of promises you can't keep, max out your creative problem-solving abilities, and hope like hell you can get it done enough to show before you completely run out of money and friends.
While we enjoyed the film quite a lot the dude was not terribly happy with it (all he could see at that point were mistakes and limitations), and was beyond broke (that's why he was couch-surfing his way through the cities he was showing in, he could barely afford transportation to the next city).
Film making technology has come a long, long way since then, so you could probably make a similar quality film much easier and cheaper now (I wouldn't be surprised if the expensive cameras he was renting at the time are outclassed by what you can do now with a nice phone and a second-hand Canon). But the rest is probably pretty similar. Lots of dollar-stretching and creative problem-solving.