The practicality of Anarchism is a huge question. I am not an anarchist myself but I do sympathize with their struggles and see some of their arguments.
Anarchism has been practised effectively in Ukraine just after World War I and in Spain just before World War II. Spain is the best example. The Spanish Republican government collapsed with a military uprising lead by General Franco, who later became the fascist ruler of Spain. In response, various anti-fascist movements combined with the large scale anarchist movement and fought the Fascists with international help and held off for three years. Barcelona developed an interesting system, one of their first actions was to burn money. They figured that without money and greed, theft and governments became less of problem. Labour was organized by guilds/unions who made agreements with each other to insure the flow of services. A simple example was the farmers guild made an agreement with the grocers guild to grant produce as required. Workers would then go to grocers and receive food or cooking at communal restaurants.
Each worker in a union had direct say as to what was happening. There was no real advantage to screwing with the system. You helped out and you were provided for. Why steal when produce is given to you? Why lead a life of crime when education is free? The people of Spain also feared the march of the fascists. They weren't worried about their own advancement but with saving themselves from the fascist bombs and death camps. In this struggle one of the more successful anarchist movements was achieved until the Nazis were able to help topple the people of Madrid.
Anarchists fall into many categories, anarcho-capitalist, anarcho-syndicalists, anarcho-socialists etc. One solution to the problem of greed and theft is to abolish money and the struggle for resources. Anarchists also don't oppose organization, they oppose vertical organization (i.e I am Kind and you do as I say; opposed to we need to do this task how do you think we should do it?)
Anarchism is an interesting concept. I have heard anarchists ask, you live like one most of the day. The government intervenes to give you a speeding ticket or to demand taxes to kill people in a foreign land. It's an interesting argument and you can take it as you wish.