There are a number of misconceptions about anarchy, one of which is the idea that there are not consequences for your actions. This is false. Believing that government is the only arbiter of justice is an insult to the concept of justice. We have established that ethics can be derived rationally, so we can then rationally determine what constitutes a violation of those ethics and what might constitute a just resolution to the violation. As individuals capable of rational thought, we do not need one organization with a monopoly on force to tell us how to live or arbitrate disputes.
In our modern society, we are so conditioned to believe that the reasons people do not commit crime is because of the police that we lose our understanding of morality or our natural internalization of it. If police presence was really the reason for low crime, then in areas with the most police there would be the least crime. In fact the opposite is true. In white suburbia, there are maybe three cops that patrol localities of 30,000 plus people, and there is virtually no crime. There may be occasional property crime, but certainly no murders. However, if you look at inner city Chicago, Baltimore, Washington D.C., and Los Angeles, there are hundreds, if not thousands of cops, and crime is rampant. Police presence is a symptom of criminality, not its remedy. So why then are the peaceful places peaceful and the violent places violent?
The answer lies within the people that live in the respective areas. The individuals that live in the suburbs are more capable and thus more apt to internalize morality. Earning money requires deferral of gratification, whereas stealing it results in immediate gratification. Earning money guarantees a steadier stream of consistent and potentially increasing income, whereas theft guarantees nothing. Earning money requires cooperation and respect of your fellow individuals, whereas theft requires only that your fellow individuals do not know you are the thief. If you have the capacity to rationally understand this, then you are far more likely to live in the suburbs, or a community of respectively low criminality.
In order for anarchy to succeed we need to live in a world where a plurality of people understand the aforementioned concepts and are willing to respect them. Thankfully, we do live in such a world. The majority of people, at least in America, do not commit crimes because they know they are wrong. Despite what your initial thoughts might be about your fellow citizens, if you put them to task, they will not steal from you, murder you, or rape you. In fact, they will most likely be as opposed to those ideas as you are. This is a good thing. It means we do not need to convince people of morality; we simply need them to recognize that most other people agree with and share their outlook on the topic. Recognizing this, all of the systems necessary to arbitrate disputes will arise organically. We have the power to thrive in a state of anarchy, all we need to do is have the courage to recognize it. Only then can we flourish!