If you don't mind it, being nomadic might be a good option for a minimalist. A lot of people live happy lives that way, get to experience interesting adventures, and meet all kinds of new people. All you will have to spend money on would be the initial supplies to get started, such as a decent backpack with a frame, a sturdy pair of shoes, good socks, something for keeping dry, something for keeping warm, and maybe a lightweight musical instrument to make getting spare change easier. (Street performers have better luck than the bums with signs unless the sign is especially clever.) My first recommendation when doing this for the first time is to find someone who is already living this way, befriend that person, and get as much information as you can about the lifestyle. If you trust him/her, and if s/he trusts you enough to allow it, travel with that person instead of going alone. Your adventure will involve a lot of walking and possibly some hitchhiking, unless you intend to stay in one area for a while, so make sure your shoes are practical. I can't stress this enough.
Food:
Dumpster diving for food is free, and sometimes businesses throw away perfectly good expired stuff if you can find a place that doesn't put a lock on their trash. When I was in Portland, some bakeries even left their extra bread in bags by the door, and I had fancy olive bread whenever I wanted it without spending anything on food. Also, the people at Food Not Bombs had vegan feeds in the park on certain days, and sometimes brought the things they would find in dumpsters if there was extra. We usually got expired Odwalla juice, lots of slightly bruised produce, and packs of seasoned tofu, as well as interesting breakfast wraps and other foods that I think might have been made by the Hare Krishnas, who were also really nice and liked to invite strangers over to eat with them. There are also normal charities to feed homeless people if you end up unable to find anything on your own. When I was living in Portland, I almost never had to spend any money at all on food.
Shelter:
As long as the weather is nice, It is possible to sleep in parks if you can avoid being seen and can find one without a sprinkler system that comes on at night (I had that happen to me once while sleeping under a tree. lol), or to camp out unnoticed in wooded areas alongside roads. You might want to team up with other squatters in the area who already know what they are doing. They might be able to suggest more resources. If you are living somewhere that gets cold, make sure you are somewhere warm or have shelter by winter, of course.
CouchSurfing - Participate in Creating a Better World, One Couch At A Time <---- I plan to try it this way someday, and to wander on foot from town to town sleeping at people's houses, doing chores for them along the way. It would freak out my parents, though, because of the dangers involved. I've done a little hitchhiking, but haven't ever lived as freely as I want to.
