A 'hacktivist' claiming to be participating in Operation Payback, in New York. Photograph: Sipa Press/Rex Features

It is being described as the first great cyber war: an online collision between some of the world's greatest brands and a little-known, poorly understood group of "hacktivists" trying to bring down companies from the comfort of their bedrooms.

The hacker group behind the attacks goes by the name of Anonymous. This week it declared its goal to be "infowar" and said: "In war, there are bystanders that get hit."

As the name suggests, Anonymous is not a group with high-profile members. Its composition is multinational: a 16-year-old Dutch boy was arrested this week on suspicion of bringing down the websites of MasterCard and Visa in support of WikiLeaks. The family computer he is suspected of using has been seized.

Although its attacks seem co-ordinated, it is not clear who is leading the group and its members have only the faintest of ideas about its goals. Its most audacious effort, an attempt to bring down Amazon, was thwarted after members could not agree which site to attack next.

Described by one insider as "complex, puerile, bizarre and chaotic", Anonymous propelled itself into the public consciousness this week with a succession of attacks on major US institutions – but it has been striking fear into the heart of Scientologists and copyright enforcement agencies for years. Earlier this year, members forced the Ministry of Sound websites offline after the dance music group tried to prevent piracy of its catalogue.

Anonymous was born on the influential internet messageboard 4chan, a forum popular with hackers and gamers, in 2003. The group's name is a nod to 4chan's early days, when any individuals who posted to its forums and chose not to identify themselves were automatically dubbed "Anonymous". But the ephemeral group, which picks up causes "whenever it feels like it", has now "gone beyond 4chan into something bigger", an active Anonymous member told the Guardian.

Anonymous has no command structure. Members communicate using secure chat-rooms, the location of which constantly move to evade detection. The movement works through "organised chaos" where individuals post ideas and new targets to attack, and wait to see the response. Eventually popular ideas generate action.

The technique is simple. Members target a website with repeated requests to load its pages until the site under attack can no longer cope. A site can be hit with thousands of requests a second, and this week MasterCard was among the companies that found its website could not cope. These are known as "distributed denial of service attacks" – DDoS, an acronym that is ubiquitous in the hacker community. Those wanting to participate download a special software package – LOIC, or low orbit ion cannon – which takes only a few minutes to be ready to use.

Coldblood, a British member, set up chat servers for Anonymous so the group could plan attacks on the Church of Scientology in January 2008 when it attempted to remove from the internet parts of an interview with Tom Cruise, its most famous member.

"The Scientology stuff was a couple of thousand people at its peak. But we've just seen it spiral into what it is now. It's actually astounding me that it's grown this quickly," says Coldblood.

Downloads of the LOIC software have grown 60-fold, from 390 to 23,479 in the last week.

For the targets, which this week also included the Swedish prosecution authority – which is pursuing sexual assault cases against WikiLeaks founder Julian Assange – and the PayPal payments system, it can mean their business is halted for hours if not days.

The Anonymous movement is approaching a tipping point in its campaign. So unwieldy, reactive and vitriolic is the group that members often turn their weaponry on each other. Factions "attack each other regularly," Coldblood says.

The group can swell and contract, splinter and re-form – then muster an illegal attack that severely disables expensively administered websites owned by multinational corporations. It is the newest form of anarchic rebellion.

"It is political activism to an extent," the 22-year-old hacker explains. "But lots of the people just do it for a laugh really – there's the whole mentality of 'did it for the lulz'." Lulz, for the uninitiated, is short for laugh out loud misspelt, but its meaning is closer to schadenfreude.

However, Coldblood believes that the days of sheer anarchism are numbered, and that Anonymous is becoming more organised. "Now it's moved more to the political side, which wants to take things a bit more seriously. It already has effectively split inside but it hasn't on the outside. You cut one section off and it'll grow back."

When their sites go down, multinational victims can do little but wait for the bombardment to subside – and invest in more attack-proof servers. Microsoft will next week release a tranche of security updates in an attempt to stem the propagation of DDoS attacks.

More than 1,000 sites are mirroring WikiLeaks to ensure it stays online in the face of capitulation attempts. The "infowar" has pitted amateur hackers against some of the western world's greatest institutions. But a more significant, perhaps fearsome, war would be one that succeeded in marshalling the full muscle and might of Anonymous behind its campaigns.