The brief version, with the exact search queries you'll want bracketed: you send a [debt validation letter] under the FCRA to the CRAs. This starts a 30 day clock, during which time they have to get to the reporter and receive evidence from the reporter that you actually own the debt. If that clock expires, the CRAs must remove that tradeline from your report and never reinstate it. Roughly simultaneously with that letter, you send the collection agency a [FDCPA dispute letter], and allege specifically that you have "No recollection of the particulars of the debt" (this stops short of saying "It isn't mine"), request documentation of it, and -- this is the magic part -- remind them that the FDCPA means they have to stop collection activities until they've produced docs for you. Collection activities include responding to inquiries from the CRAs. If the CRA comes back to you with a "We validated the debt with the reporter." prior to you hearing from the reporter directly, you've got documentary evidence of a per-se violation of the FDCPA, which you can use to get the debt discharged and statutory damages (if you sue) or just threaten to do that in return for the reporter agreeing to tell the CRA to delete the tradeline.
No response from the CRA? You watch your mail box like a hawk for the next 30 days. Odds are, you'll get nothing back from the reporter in that timeframe, because most debt collection agencies are poorly organized and can't find the original documentation for the debt in their files quickly enough. Many simply won't have original documentation -- they just have a CSV file from the original lender listing people and amounts.
If you get nothing back from the reporter in 30 days, game over, you win. The CRA is now legally required to delete the tradeline and never put it back. Sometimes you have to send a few pieces of mail to get this to stick. You will probably follow-up on this with a second letter to the reporter, asserting the FDCPA right to not receive any communication from them which is inconvenient, and you'll tell them that all communication is inconvenient. (This letter is sometimes referred to as a [FOAD letter], for eff-off-and-die.) The reporter's only possible choices at that point are to abandon collection attempts entirely or sue you. If they sue you prior to sending validation, that was a very bad move, because that is a per-se FDCPA violation and means your debt will be voided. (That assumes you owe it in the first place. Lots of the people doing these mechanics actually did owe the debt at one point, but are betting that it can't be conveniently demonstrated that they owe the debt.)
If the reporter sends a letter: "Uh, we have you in a CSV file." you wait patiently until day 31 then say "You've failed to produce documentary evidence of this debt under the FDCPA. Accordingly, you're barred from attempting to collect on it. If you dispute that this is how the FDCPA works, meet me in any court of competent jurisdiction because I have the certified mail return receipt from the letter I sent you and every judge in the United States can count to 30." and then you file that with the CRA alleging "This debt on my credit report is invalid." The CRA will get in touch with the debt collection company, have their attempt timeout, and nuke the trade line. You now still technically speaking owe money but you owe it to someone who can't collect on the debt, (licitly [+]) sell it, or report it against your credit.
I just outlined the semi-abusive use of those two laws, but the perfectly legitimate use (for resolving situations like mine, where my credit report was alleging that I owed $X00,000 in debts dating to before I was born) is structurally similar. My dropbox still has 30 PDFs for letters I sent to the 3 CRAs, several banks, and a few debt collection companies disputing the information on my report and taking polite professional notice that there was an easy way out of this predicament for them but that if they weren't willing to play ball on that I was well aware of the mechanics of the hard way.
[+] Owing more to disorganization and incompetence than malice, many debt collection companies will in fact sell debts which they're not longer legally entitled to. This happened to me twice. I sent out two "intent to sue" letters and they fixed the problem within a week.
[Edit: I last did this in 2006 and my recollection on some of the steps I took was faulty, so I've corrected them above and made it a little more flow-charty.]