Touchdown. Now what.
A few short notes on how to get yourself from the Tokyo airports, and a few others I've used, to where you want to be. It's not too complicated really. Just make sure to keep track of what airport you're leaving from. The Osaka/Kansai mixup is a classic and you don't want to find out when it's too late.
NARITA AIRPORT – NRT
If you have a Rail Pass voucher and want to activate your pass right away, do so before leaving the airport and have the staff book a seat for you on the Narita Express. Trains don't run too often so you might want to plan ahead using the time table. If you don't have a voucher, or don't want to activate it yet, simply buy a ticket for the Narita Express. You typically want to go to either Tokyo Station, Shibuya or Shinjuku depending on where your lodging happens to be.
(There is a fast and futuristic option too, the Keisei Skyliner train. It orients every seat automatically, looks great, but only gets you to Ueno Station, so you won't be using that unless you are going to someplace close to Ueno.)
JR East Travel Service Center, Narita – locations in Terminal 1 and 2, and opening hours
HANEDA AIRPORT – HND
If your inbound flight touches down at Haneda, you're basically already in Tokyo. A good way to get to where you need to be is to board the monorail to Hamamatsucho station and get a cab from there. Rail Passes are valid on the monorail and vouchers can be redeemed at the airport (as of early 2016, the relevant JR East counter closes at 18:45).
- JR East Travel Service Center, Haneda – location and opening hours
OSAKA – KIX
Flying into Osaka is a decent option if you want to kick things off with a tour of central or southern Japan. A variety of railway lines will get you straight to downtown Osaka, Kobe or Kyoto and rail pass vouchers can be redeemed at the airport. If the goal is to get yourself to Namba Station, use the Rapi:t line. But be aware that you can't use the rail pass on that line.
Note: If you end up departing from Osaka, be sure to keep track of what airport you're actually going to be using. The super-confusingly named Osaka International Airport (ITM) only serves domestic routes so if you're going overseas, the one you want is the Kansai International Airport (KIX).
FUKUOKA – FUK
The airport is pretty much right in the middle of Fukuoka and transports are easy. Taxis are a good option if you're staying in downtown Fukuoka. And there's a subway station underneath the domestic terminal. If you touch down at the international one and want to use the subway, simply jump on the free and frequent shuttle service connecting the terminals.
KAGOSHIMA – KOJ
Going from the airport to downtown Kagoshima takes about 45 minutes, either by taxi (JPY 10,000-ish) or one of the two Bus services. I no longer use the Kagoshima airport since it's a bit of a hassle. These days I fly into Fukuoka, jump on the Shinkansen serivce down to Kagoshima and boom, done.