The Japanese knew what had happened after the Hiroshima bombing because America told them, essentially. A leaflet was created that described the weapon as an atomic bomb that was "the equivalent in explosive power to what 2,000 of our giant B-29's can carry on a single mission." These were dropped from T-3 leaflet bombs to 47 Japanese cities with a population of over 100,000. Unfortunately, the printing and delivery of six million leaflets was a time consuming process, delayed even further by a shortage of leaflet bombs, and some cities did not receive the information in a timely fashion. Nagasaki, for example, was hit by its Atomic bomb on August 9th, while the flyer warning of the strikes didn't reach them till August 10th. However, the printed message was also broadcast every 15 minutes by Radio Saipan and likely began the same day as the Hiroshima bombing.

Full leaflet text

It's also important to note that the Japanese did have their own research into the feasibility of a fission weapon, although they eventually concluded that neither Germany or America had the requisite spare industrial capacity to produce atomic bombs in time to determine the course of the war. Research was then sidelined into things like radar and nuclear propulsion instead. However, there would have been Japanese scientists who'd have a reasonable understanding of how such a weapon would have worked.

Still, among the average military officer, there was quite a bit of confusion as to how the weapons operated. Lt. Marcus McDilda, a P-51 pilot who was shot down and captured the day after Hiroshima, experienced torture by Japanese officers intent on discovering how the atomic bombs worked. Faced with decapitation, he fabricated a story about how the US had worked out a way to separate negative and positive charges, kept apart by a lead sheet, and that with the removal of the sheet, the intermingling of the charges caused the explosion. He also claimed the United States had 100 more atomic bombs and Tokyo and Kyoto were the next targets. He was sent to Tokyo, where he was questioned by a Japanese physicist who realized that McDilda had no idea how the bomb worked. McDilda revealed that he had made the story up, and he and the physicist both shared a laugh.

Sources:

Rhodes, Richard (1986). The Making of the Atomic Bomb. New York, NY: Simon and Schuster

Hagen, Jerome T. (2005). War in the Pacific: America at War Volume 1, Honolulu, Hawaii: Hawaii Pacific University