Right before Harry goes off to Hogwarts in Prisoner of Azkaban, Arthur pulls him aside and attempts to make him promise not to go looking for Sirius Black "whatever [he] might hear." To this point of the novel, we could believe Arthur's worries that Harry will pursue Black stem from merely from the fact that Black was allegedly a high-up Death Eater... and Harry has a propensity to dole out his own servings of vigilante justice.
However, after overhearing the conversation in the Three Broomsticks and learning that Sirius "betrayed" the Potters, Harry asks himself:
Why had nobody ever told him? Dumbledore, Hagrid, Mr. Weasley, Cornelius Fudge … why hadn’t anyone ever mentioned the fact that Harry’s parents had died because their best friend had betrayed them?
Harry Potter and the Prisoner of Azkaban (page 263, paperback US Edition).
At least by strong insinuation, JKR is telling us that Mr. Weasley was, in fact, worried that Harry would find out this particular information.
So, as this information was so privileged, how did Arthur Weasley, who was not in the original Order of the Phoenix, know it?
Best I can come up with: His work at the Ministry of Magic? Could he have heard Dumbledore's testimony?
Came across a detail I had forgotten: Pettigrew yelled it out for everyone to hear... people at the Ministry would have learned this.