Certainly the quickest (and perhaps the cheapest) way is to fly. The alternatives involve taking the Shinkansen to Hakata and then express trains on down. The whole thing would take you about 6 hours at least, since it is 3:00 or so from Osaka to Hakata on the Nozomi. But its a fun ride. If you want cheap-cheap, you can always take slow trains. I took one once, in my salad days, from Tokyo to Nagasaki. 18 memorable hours. Another one was from Ueno to Sapporo, which was only about 14 hours, including a stop for sushi at the Noboribetsu fish market and a soak at the onsen.