Member Rara Avis
There are two ways, I think, to approach this, one perfectly safe and the other pretty much safe.
Perfectly Safe: Change the fictional representation of the character and events so much that no one could possibly recognize your source (especially your source). Unfortunately, this isn't always possible. Sometimes, a characteristic of your source is both very recognizable and yet vital to the story (else the events would not have unfolded the same way). Sometimes, a characteristic is unique and unerringly identifies the source (if you base a story on Neil Armstrong, making your fictional character the first man to walk on the moon might let the cat out of the bag). But I think these are unusual circumstances, and in MOST instances any character or sequence of events can be changed enough to make them, if not unrecognizable, at least very questionable.
Pretty Much Safe: Don't even try to hide either the characters or events, but instead report them as news. News, in and of itself, cannot be copyrighted, and anyone is free to report and even interpret current or past events. The caveat here, as in any reporting, is to scrupulously avoid libel. Be very, very sure of your facts.