Arctic Monkeys are true children of the internet - nobodies who gave away their music online, they're now one of the fastest-selling acts ever. Jim Carroll finds out from Monkey boys Alex and Matt, both still in their teens, if they're ready for the madness that fame has in store for them.

SO what's the strangest thing that has happened to you so far? The two Arctic Monkeys have answers for that question almost immediately. "There's this bar in Dundee called the Arctic Bar, right," says singer Alex Turner. "And there's a big sign outside the bar with 'Arctic' written in huge letters. Someone spraypainted 'monkeys' under it and sent us a photo. That's pretty mad."

"And there's an indie club in London called I Bet You Look Good on the Dancefloor. That's weird," chips in drummer Matt Helders.

"I'm sure someone has got an Arctic Monkeys tattoo by now," adds Turner.

"That would be cool to see. Didn't someone we know get a Yeah Yeah Yeahs tattoo?"

As the pair talk, you get the strong sense that this reply may have to be updated. It's a Tuesday afternoon in Dublin and this is the week when the Year of the Monkey begins in earnest.

The previous day, 118,501 copies of the Sheffield band's debut album, Whatever People Say I Am, That's What I'm Not, were sold in the space of 24 hours in Britain. By the following Sunday, that figure will have reached over 360,000, making it the fastest selling debut album in UK chart history. Similar sales were also recorded in other European countries.

But those statistics are just the tip of this Arctic iceberg. All week, there is absolutely no way you can escape these four kids. After all, there are very few people in the pop punditry business who don't have an opinion to offer on the Monkeys - and there are very few of these opinions which are not heard.

Radio stations, TV shows, newspapers, magazines and internet sites are overloaded with Monkey talk, as the band are debated, discussed, derided, disputed and dissected. Are they the new Beatles? Are they better than The Beatles? Are they - God forbid - bigger than The Beatles? Even BBC's Newsnight and pop-culture economist David McWilliams jostle to have their say on a band with two No 1 hit singles and a blockbuster album.

Then there's the whole internet angle. The band gave away CDs of their early demos to fans, leading to passionate word-of-mouth recommendations and much online song-swapping and file-sharing.

As a consequence, the internet has found its way into every single story about the band, sparking hundreds of ill-informed pieces about how giving your music away for free online is the future for the music industry. Such comments overlook the fact that thousands of bands already do this, but without the same success rate as the Monkeys. Still, there is something to be said about a best-selling album coming after thousands of people have downloaded the music for free.

Two surreal snapshots stand out in a week of excess silliness. One is the rumour played out on music industry website Record of the Day that the band's witty lyrics are not their own work but rather written by a shadowy svengali. This conspiracy theory goes on for a few days (including a bizarre sub-conspiracy theory that the lyrics theory is actually some kind of sinister marketing ploy) before predictably running out of steam.

The other is an interview with Lauren Bradwell in the News of the World. "This stunning blonde was the secret inspiration for a hit song by No 1 pop sensation Arctic Monkeys".

Lauren describes Alex as "a really sweet lad, a real gentleman who was kind and treated me with respect". But after four months of innocent fun, she dropped him in favour of someone who owned a Peugeot 405. "Now I wish I'd stayed with Alex," she wailed to the paper. Given how Turner described the relationship in Bigger Boys and Stolen Sweethearts, there is unlikely to be a reunion, but there may well be another song.

In a small, dreary, untidy dressing-room in Dublin's Ambassador, you'd never guess that you were in the presence of a pop sensation. Both Turner and Helders are friendly and polite but, like most 19-year-olds, are not very comfortable answering questions about themselves or what's happening to their band. They would probably prefer to be scoffing Chinese food in the background, like guitarist Jamie Cook, or somewhere else entirely, like bassist Andy Nicholson.

"It still feels weird to be talking about ourselves so much," says Turner at one point. You hope someone has warned him about the meet-and-greet promotional circus in the US, which will be his lot for the next few months if he wants to make an impact over there.

But perhaps the Monkeys harbour an innocent hope that the music will do the meeting and greeting for them in the US of A. After all, leaving aside the spurned sweethearts, music industry puffing and hysterical sensationalism, it's all come down to the songs. No one is buying their album because Jeremy Paxman is sardonically raising his left eyebrow about it. They're buying it because songs like I Bet You Look Good on the Dancefloor are bloody fantastic.

Put simply, Whatever People Say I Am, That's What I'm Not is the best British debut album to come our way since The Stone Roses. The music is dashing, the playing remarkable and the energy thrilling, but it's the songs about modern life in an everyday northern town which will take your breath away and stick in your head for weeks. It's as if Paul Shameless Abbott had picked up a guitar and let loose.

Turner's tales of trendy bands (Fake Tales of San Francisco), Saturday night run-ins with the police (Riot Van), grumpy bouncers (From the Ritz to the Rubble), a taxi trip home from town (Red Light Indicates Doors Are Secured) or the narky face on a miffed girlfriend (Mardy Bum) are peerless. Very few new songwriters are penning their tunes with the nonchalant wit, infectious verve, bittersweet romance and fantastic eye for detail which Turner employs.

"They're just observations," says Turner of his lyrics. "It makes sense to write about what I see around me and what I know. It's a bit like hip-hop in that sense. You get the words, you make sure they make sense, you get the words to rhyme and away you go."

The hip-hop reference is not a glib one. The band's fondness for everyone from Roots Manuva to Dr Dre has been well documented, and they usually come onstage to the sound of Dre's Xxplosive or Next Century.

When Turner talks about songs he admires, it's the lyrics which grab him every time. "I don't think there's any one songwriter that I've really admired. I really like Oasis' Don't Look Back in Anger. That's a great song. Sometimes lines will jump out at me and I'll wish I'd written that or something like it."

At their very first gig, most of the songs they played were cover versions.That was back in June 2003 at a Sheffield pub called The Grapes. Tunes from The White Stripes, The Datsuns, The Beatles and The Undertones bulked out their eight-song set. They knew that they were nothing to write home about, but they knew their own songs did sound better.

"The only reason we were doing covers was because we didn't have enough songs," says Helders. "From the very start, we realised we could do our own stuff much better than the covers we were murdering."

At first, their own songs sounded just like those covers. "You'd hear stuff that was out at the time and you'd try to write summat like that," says Turner. "But there were limitations because we couldn't play whatever we wanted to play because we just weren't good enough, so that had an effect on the songs we were writing. We had to write songs we could play."

At that time, the band members were in college (Helders studied music technology and Turner took psychology and English classes) and everyone they knew seemed to be in a band. "You'd realise your mate was in a band so you think it's not that hard," says Helders. "At the start, we just went with the flow. There really wasn't a great deal to separate us from those other bands. Some of them were a lot better than us. We used to go to see them and admire them - they were what we wanted to be."

That pecking order changed as the Monkeys spent more time writing and rehearsing. By summer 2004 they were no longer just another college act and were gigging throughout the north of England and Scotland. By January 2005 the industry buzz had begun. Enter Laurence Bell's Domino label, fresh from massive worldwide success with Franz Ferdinand. It was time for a whole new chapter to begin.

"When we started, it used to be such a great achievement for us just to get a gig", recalls Turner. "Then we started to get better and better and more people began to notice us. The big thing then was about recording some songs. Then it was about getting a release, and that was sorted with the Five Minutes With Arctic Monkeys single. Then we wanted to make an album. And now, all of this is happening."

Turner gestures towards the door with a water bottle and shakes his head. It's obvious that he finds it all a little surreal. He's beginning to realise that normal behaviour has been suspended and may not resume for quite some time.

Even their Dublin shows, part of an NME-endorsed tour, now seem somewhat ludicrous, especially as the band are second on the bill to the humdrum Maximo Park. Things have changed since the tour was booked. Things change extremely fast when you're an Arctic Monkey.

But it's the little things that are also hard to adjust to, like all the comparisons that have come their way. Turner says he's usually never heard of most of the bands that people think they sound like.

"It happens a lot. We just look at one another and go who are they? Musically, there's loads of stuff that we don't know about yet. Like The Buzzcocks. I'd never heard of them until someone said we sounded like them so I went off and checked them out. Do I think we sound like them? Nah, not at all!"

Hopefully they know it's just going to get weirder. The next couple of months will see them touring Europe, the US and Japan, while a UK tour in April is already sold out. The album is set to be the sound of the summer and may well become one of those albums which signify a changing of the guard.

As Maximo Park found out on this tour, there are few bands who can follow the Monkeys right now.

Whatever People Say I Am, That's What I'm Not is on Domino