Well, during an argument is good. You create conflict at the same time that one character (hitting below the belt, justifiably or not) provides the other's backstory. Or, on the flip side, small talk:
"How's your mom?"
"Don't be an asshole. You know she's dead." Ten years ago today, in fact.
If it doesn't seem to fit naturally into the scene/conversation, don't force it.
The first question you really need to ask yourself is, how much backstory does the reader need to know? We know our characters backwards and forwards, but does the reader really need to? I'm struggling with that problem myself right now. In a perfect world you can hint at a backstory without fully exposing it.
(reposted from a conversation yesterday)
A great example of this is Michael Connelly's "The Black Ice." In an opening scene Harry Bosch is sitting on his deck watching helicopters attempt to extinguish a wildfire. "It reminded him of the dustoffs in Vietnam." **
This simple line adds lets the reader into one of the reasons Harry is Harry, without going into a flashback about the horrors of Vietnam.
**source- "Writing Mysteries: A Handbook by the Mystery Writers of America."