When The Meter Starts Running
The statute of limitations clock starts ticking at the time the injury occurred, regardless of the claims you make, whether that is financial harms or emotional distress (the two most consistently successful claims when suing for defamation), or something else. In most situations the cause for legal action has "accrued" on the actual date of the libel or slander, just as a for a burglary, the meter starts ticking the actual day of the burglary.
State Exceptions to Defamation Statutes of Limitations
Several states have longer periods up to 6 years in some cases to file suit for defamation in cases of medical malpractice, wrongful death, or personal injury.
Delaying the Date of Accrual
If the date of "discovery" (not to be confused with the legal process of discovery, which means squeezing information out of the other team) comes after the act, then you may be able to get the statute of limitations extended.
In this sense "discovery" means when you discovered that defamation had happened, or when it started doing you harm. There is likely to be a good bit of "shoulda-woulda-coulda" when two lawyers get to arguing. With a defective product that usually means the day the defect showed up. But with defamation it may not be as clear their lawyer shows the slander was quoted in The New York Times; your lawyer shows that you were on a two-year expedition in the Amazon rain forest. Their lawyer shows that you were in New York City for a week during those two years; your lawyer shows that you didn't meet anyone who had read the newspaper story. And so on....
Extending the Statute of Limitations
In civil cases the time limitations for the claim can be "tolled", which is somewhat like a football "time out". If you were hospitalized in a coma for a year, that's a pretty clear-cut cause for tolling the statute. Other reasons might be if you were a minor at the time, or on combat tour. Not being able to afford a lawyer seems like a good reason to have a statute tolled, though we've never seen it used.
It's easy to get the evidence for libel. You buy a back copy of the newspaper, or subpoena the video or audio tape.
If it's slander, get to work soon. Slander is more slippery than libel. People lie, make anonymous false reports to anyone from the police to child protective services or your employer, and change their stories it can take a good bit of time to collect the evidence. And unlike libel, it's not a great idea to file the lawsuit and have your lawyer start questioning everyone in sight, since that tells everyone you could be serious trouble. You want to start gathering evidence quietly at first, and collect as much as you can before turning on the legal heat.
Note for countries other than the U.S.
This website gets a lot of visitors from Commonwealth countries, Canada in particular. Some of this legal information applies to Canadian defamation, some doesn't but in most countries the statutes of limitations for libel or slander are much shorter than in the U.S., sometimes as little as six weeks.
For a thorough plain-English guide to defamation and how to deal with it, please see our report Fighting Slander, applicable in all 50 states.