Resistance is a mental state. The Matrix is designed to make it easy to accept what it tells you, and to make it hard to filter the Truth from the lies. Resisting the Matrix requires understanding its operating principles and assumptions, rejecting them, and helping others to do the same.
The Matrix is fascist, the Matrix is deceptive, and the Matrix is bureaucracy. The Matrix is essentially the rule of the institution over the individual, and in it, the rights of the individual are subordinate to the rights of the institution. Individuals have to believe (or at least not actively oppose the idea) that large corporations have the right to protect their profits above all else, and thus dictate policy and law. They have to believe that this law is just, moral, and seemingly based upon reason. Or, they have to feel unaffected by the law on an individual level. They have to accept the program, and be satisfied with the rewards given for doing so. They have to do their jobs, pay their taxes, and be content with their salary (at least to the point where their salary and the stability it provides are appealing enough to deter risking leaving the Matrix). Rejecting these beliefs is the first step in resisting the Matrix.
Furthermore, people must be insulated from the creative process. They have to forget that they are able to produce craft as individuals independent of large institutions, and they must feel entirely dependent upon the system to provide them with what they need. It is mostly through the violation of this principle that many who work with computers come to free themselves, or at least come to see the Matrix for what it is. Despite being products of the Matrix (for the most part), computers and the Internet enable humans to create individual works on a global scale: independent media, self-publishing, Free Open Source Software, computer music, computer art and graphics, and so on. Computers also enable independent people to communicate and build human-serving social structures outside of the Matrix.
However, note that computers aren't the only means of accomplishing this, and this time period isn't the first one of Exodus. In the 1960s, for example, people departed from the Matrix en-mass and independently created art, culture, and music, largely catalyzed by psychedelic drugs. Unfortunately, much of this structure collapsed due to a number of reasons, the main one being the hasty, ill-considered and unsustainable manner of its construction and the subsequent institutional and legal backlash. Miraculously, however, many of the core ideas have persisted, and their proliferation is largely the reason I am Aware and able to write this document today. It would seem that the present catalyst is a combination of the Internet and again psychedelics. Both of these phenomena provide a way of disconnecting yourself from the programmed reality and assumptions of the Matrix and taking your perceptions into your own hands. However, your "perception" is nothing but your individual dream that you have created as you have gone through life. There is the dream of the society that has been passed down generation after generation and instilled into your mind by your parents, friends, schools, and institutions. And then there is your individual dream. Each step of the way in your life you have lived subjectively, and depending upon how and where you grew up, who you hung around with, and the habits you formed, you created your little dream. Your "theory" on life while you stay completely unconscious of this. Everything that you think is "you", "I",
"me", and everything you believe that you identify with is simply not you. It is not the truth. It is part of the giant web of individual dreams that everyone is in the clutches of on our planet. This is one of the main reasons why this world is the way it is, why it is so chaotic. You will scorn anyone who does not dream what you dream of, and someone will do the same to you. It is impossible for us to live the same individual dream because we cannot know everything about each other down to our core. It is a constant fog that grows bigger and bigger and more dense as each day passes. It is your ego and it is my ego. The dream is not real. If we want to even begin to understand what it means to exist as a human being on this planet and evolve, this truth must be learned and it is just the beginning. Somewhere along the way, the entities that have been running the show figured out how the ego works, and they have been doing a damn good job at distracting us from trying to find a way out of our dreams and the dream of society. Psychedelics are simply a tool, but one of many to truly explore and expand your consciousness. However, whether it be psychedelic substances or meditation, it is not the ultimate answer. It is simply showing you the door, but it is your choice whether or not you want to enter into the other side.
To persist, the Matrix requires control, and in democratic societies it maintains this control by filtering people's view of reality through corporate-owned mass media and television. 
In essence, the Matrix requires a form of thought control, but not in the science fiction sense. Instead, it achieves an effective enough manner of thought control by manufacturing consent. The large majority of the public has to "buy in". They have to believe that the news media give them an accurate picture of the world. And by and large, they do believe this. Everything the general public knows about the world, they know through the Matrix. The symbols and images the Matrix presents to them have become more real than reality itself. Hence the popularity of the ungodly abomination that is Reality TV.
Note that while some media outlets do actively promote a political agenda of domination and control, on the whole it is not through some grand conspiracy that this process (or any process of the Matrix) functions. It is simply the way mass media is organized. Mass media is a machine that exists as a profit maximizing entity, and the most profitable news (and the cheapest news to produce) is recycled soundbytes and pre-packaged press releases from corporations and government. Furthermore, in the interest of preserving its revenue stream, news media cannot allow the public to hold any opinion that may threaten the authority and policy of government or the profitability of their sponsors, which are also machines of the Matrix and almost always directly involved in the business of domination and control. Thus the media must perpetuate the status quo. No news is good news.
Understanding this bias in the media is key to undoing the filter it applies. Consider who the advertisers and sponsors are. 
Beware of press releases disguised as investigative reporting. When possible, confirm mainstream, corporate produced stories with coverage from places like IndyMedia (go local), Wikinews, GNN, Politech, Free Speech TV, Democracy Now, Free Speech Radio News, and FAIR. A lot of the time these sources also cover many eye-popping items that for some reason don't even receive mention on corporate news media.
Last, and most assuredly not least, the Matrix seeks to identify and know its members at all times, in a misguided attempt to maintain control. It demands total surrender of your privacy to function in it. It is by breaking this last property of the Matrix that we come to truly free ourselves from it; to create economies, communication, and culture independent of its control.
Of course, the ultimate form of resistance is to fully disconnect from any and all dependence upon and allegiance to government and institution; to remove yourself from the power structure of the Matrix, and contribute your economic output to resistance economies. It is this form of resistance that faces the most violent opposition from the Matrix, since providing this economic power is the primary function of Humanity, as it sees it.
Unfortunately for many this form of resistance is simply unattainable due to family and social ties, especially starting from your first realization of the size and scope of the Matrix. However, unlike in movie, it is possible to liberate yourself gradually instead of immediately, and in some cases this can prove easier than an 'all-at-once' attempt. It starts with disconnecting. Cut out TV from your life entirely, especially TV news and Reality TV shows. You should be able to get all your information and entertainment from the web, or from real reality (or from the occasional movie). Avoid chain stores where possible, especially for food. Supporting smaller (especially sustainable) business keeps entrepreneurial and independent business spirit alive. Getting and staying out of debt (especially debt without equity, or rapidly depreciating equity such as car loans) is crucial, as debt is a primary mechanism the Matrix uses to ensure your obedience. Also, if you are a salaried employee, working a 40 hour (or perhaps even 35) hour work week can be a big start to declaring your freedom from the machine and the corporate American peer-pressure to be a diligent slave. It also frees up huge amounts of mental energy which is then available for resistance.
From here, a limited form of resistance whereby you leave the Matrix for short periods of time (long enough to conduct purchases, business transactions, and communications with the underground) is well within the reach of all computer literate individuals, and functioning as a consumer is sufficiently supportive of the Anonymous Economy for it to be sustainable. Moreover, the probability of discovery of this sort of activity can be reduced as much as you choose. Doing this effectively is the subject of this HOWTO.
As you progress, you will notice yourself developing one or more separate identities, or pseudonyms. It is best to build as much insulation between these nyms as possible. They shouldn't appear to know each other, shouldn't really talk about the same stuff or buy the same things, and above all should be diligently separated from your original physical identity. Maintain different wallets, bags, user accounts and possibly even computers. In short, develop one or more Tyler Durdens, except without all the insanity, self-destruction, and sociopathic behavior. Or with it, if it helps.
The adept and the entrepreneurial will find it an easy step from here to total freedom. The next stage is to go into business for yourself. It doesn't have to be an anonymous business, but those who manage such an achievement do enjoy the satisfaction that they are directly subverting the Matrix and helping to weaken its hold on everyone.