Before you go
Bring cash. Getting hold of it while in Japan might require more logistics than you think.
Wall sockets are US style, 110V.
No need to tip anywhere, anytime.
Book an LTE pocket wifi device for rental and have it sent to your hotel or pick it up at the airport.
Get a Rail Pass if your plan includes travelling across Japan. And you have to get it before you get there.
Sign up for the Japanese Starbucks Wifi service, doing so on-site requires roaming.
Remember, the Japanese use ✕ for no (indicate with your index fingers crossed), ◯ for yes (indicate using 👌). They're very, very polite and will generally do whatever it takes to understand your needs.
At the airport
Narita – getting yourself to Tokyo: 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. If you don't have a voucher, or don't want to activate it yet, you probably want to buy a ticket for the Narita Express. Trains don't run too often. Be sure to check the Narita Express time table if you want to optimize things a bit and plan ahead. There's another, faster option – the Skyliner – but it only gets you to Ueno (a bit off compared to the major stations).
Haneda – getting yourself to Tokyo: You're basically already there. 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.
If you do the pocket wifi renting thing, pick up your device prior to leaving the airport. If you haven't booked a device they're usually able to hook you up with one anyway.
Good to know
Get yourself a Pasmo card from a ticket machine (usually found in subway or railway stations) and charge it with a few thousand yen, then simply blip your way through the public transport gates. And pay for stuff – it's accepted by vending machines, convenience stores and most but not all Taxis.
Taxis are absolutely everywhere. They don't always accept credit cards or Pasmo cards, check for the appropriate stickers to be sure. The driver opens your door automatically, and even though they might not understand English they'll pretty much do whatever it takes to make sure you get to where you need to be.
Use Google Maps on your phone. It is, by far, the easiest way to get around with proper public transport directions built right in. This is why you either do roaming or get an LTE pocket wifi thingy. Here's an example.
If you need cash, find a Citibank or 7-eleven ATM. They're usually your best options. Most other ATMs won't accept foreign credit cards.
Stand to the left when riding escalators. This goes for pretty much all of Japan with the rather interesting exception of Osaka.
If you are using a Rail Pass to get around Japan, Google maps is still decent, but this web page gets you the shinkansen stuff in an easy way. Be sure to select "Travelling with Hikari, Sakura, Kodama and Tsubame trains". Those are the ones you're able to use with your rail pass.
The train route finder covers most local trains in detail (and sports a horrible user interface, too).
In general, credit cards are less likely to be accepted the further you get from the major cities. And it's harder to find ATMs accepting foreign credit cards, so you'll want to plan your cash logistics accordingly.
The Tokyo Pasmo card (or any other Suica card) usually works in major cities and on public transport across the country, such as the Osaka and Nagoya subway systems. It works the other way around too – if you pick up a Manaca card in Nagoya you're able to use it instead of a Pasmo card in Tokyo.