We correct the record in public, on the article that carried the error, and we say what changed.
How a correction works
When an article contains a material error of fact, the article is amended and a dated correction notice is added to the top of it, stating what was wrong and what it now says. The notice stays for the life of the article. We do not delete an article to make an error go away, and we do not amend one silently.
Where the error is in the headline, the standfirst or a figure that the piece turns on, the correction notice names it explicitly. Where it is a typographical slip that changes no meaning, the text is fixed without a notice.
Asking for a correction
Use the contact page and include the article URL, the sentence at issue, and the source that shows what the correct position is. A correction request with a source attached is acted on faster than one without, because the second one has to be researched from scratch before anything can change.
Updates that are not corrections
A developing story may be updated with new information. That is an update, not a correction, and the article carries the time it was last updated rather than a correction notice.