Most international flights to Japan serve Tokyo and Osaka, so if you’re heading to Hokkaido or Kyushu (Hokkaido in particular) it might be easier to land in Tokyo then catch a domestic flight. There are dozens of flights each day from Tokyo to Sapporo, for example, and I took one to Hakodate. Most domestic flights leave Tokyo from Haneda’s excellent, and huge, domestic terminals – a short hop on the Tokyo Monorail from the international terminal.
The biggest carriers are JAL and ANA. You can buy either through some of the big English-language online flight booking services, but I found it was far cheaper to buy direct from ANA and pay in yen – I got an advance fare far lower than the full rate being offered elsewhere.
In order to do this ANA does require a Japanese phone number; I use the Hushed app to get a temporary one on my iPhone. Booking an ANA flight direct is a two stage process: first book, then pay – don’t forget to do the latter, obviously. At the end you get a printable boarding pass.