Anarchy is, unfortunately, a very misunderstood term. Most people think it means chaos and that is simply untrue: a monarchy is a system of governance with one ruler and therefore anarchy is simply a system of governance with no rulers at all. Anarchists simply believe rulers are unnecessary. (Why, we'll explain soon. Sit still.) They do not believe that all buildings look better with fire on them or that your belongings should become our belongings. The former is called public disturbance and poor parenting. The latter is communism which is in complete opposition to the anarchist's deeply held affinity for personal freedom. 
You see, if you were to steal from another person, even to better the lives of your comrades, you would be infringing on that person's right to do what they choose with the things they've either created or earned through voluntary exchange. If you steal or condone the use of theft to aquire funding for a public endeavor which will inevitably become a facade for less public endeavors, as public endeavors always do, you are certainly not an anarchist. You are instead: an asshole. 
Some of you will, undoubtedly, ask us for solutions to many different, very specific problems, under the assumption that you're being clever. That is exactly the problem with government. There are no one-size-fits-all solutions. 
Anarchists believe in peace. Anarchists believe that all interaction ought to be voluntary and that most people, if left ungoverned, will work together to ensure all are happy and cared for. Human beings, after all, are driven by self-interest. As social creatures, we live in groups, and if a productive group member is in need of anything, it is in the best interest of every individual in said group to contribute to the longevity of said productive group member in need. This is a natural form of socialism. No two human beings are equal, however, and there will always be people, of any given group, who are more or less productive than others. Those people are entitled, again, to all they either create or earn through voluntary exchange and all that those people don't create or earn. You are free to be unproductive. You are not free to force me to pay you to be unproductive. This is a natural form of capitalism. Elements of both will always exist naturally in human ecosystems as they do in all ecosystems. 
Trees, without even having brains, understand that diversity in the soil and root neighborhood is in both their own self-interest and that of the whole forest. Trees communicate with soil microbes and other trees and plants through their root systems and trade trace minerals and carbohydrates amongst themselves, in a free market, to ensure their own survival and their ability to trade, with soil microbes and other plants, in the future. Curiously, they do all of this without the need to collect taxes of any kind at all. 
Be like trees. Be peaceful. Be an anarchist.