In most cases you will not need a visa to enter Japan, but please make sure by consulting the foreign ministry of your country, or the Exemption of Visas page of the Japan Ministry of Foreign Affairs.
For a very complete guide to Tokyo, please visit the excellent Go Tokyo website.
Tokyo has two international airports: Narita Airport (about 1h from Tokyo) and Haneda Airport (in the city area). Originally Narita was the international airport and Haneda the domestic airport, but nowadays many international airlines also use Haneda.
Narita airport is a huge complex with two terminals. Procedure through Immigration and baggage reclaim is straightforward. After recovering your baggage and going through customs, you will exit to the arrival hall. At the arrival hall, go down to the basement level 1 where the trains are leaving. The Narita Airport web page provides a detailed guide to the arrival procedure as well as detailed Terminal guides.
Haneda airport is very similar, two terminals, train departures from the basement level 1. Haneda airport provides a detailed international arrival procedure and a Terminal guide.
The GoTokyo web site has an excellent guide to go from the airport to downtown Tokyo section.
Tokyo has an excellent — if not to say overwhelming — system of public transportation. Buses might be a bit scary for people not used to riding them, but the metro and trains cover a huge area and are very comfortable to use.
If you are arriving at Narita Airport, we recommend that travelers get the special Suica & N'EX ticket and use the JR lines to Shibuya or your destination. In short, this combination gives you a N'EX ticket (high speed train from Narita to Tokyo) plus a pre-paid card for easy travelling in Tokyo.
Warning
Note that The "Suica & N'EX" package is available only
at the JR EAST Travel Service Centers
at Narita Airport Terminal 1 (8:15–19:00) and 2 (10:30–20:00).
It might look scary at the beginning, especially when one cannot read Kanji, but it is in reality a simple task. All the station names are also written in English, which helps a lot.
The steps to board a train within Tokyo are always the same.
For Suica users:
For normal tickets:
Normally — if you have paid the right amount — the ticket will not be returned and you can pass the gate.
Hint: If you are in hurry to catch a train and cannot figure out how much the fare is for your destination, you can buy the cheapest ticket (usually around 210 Yen), and before leaving the station at the destination, go to one of the always present Fare Adjustment Machines, insert your ticket and pay the remaining amount.
The GoTokyo website of course also has lots of information on travel within the city: Main transportation page, Trains (and Metro).
Again on the GoTokyo Website one can find a huge collection of excursions within Tokyo (incomplete list follows): Volunteer guides, Mountain & Onsens, Fashion & Beauty, Urban Infrastructure, and even a list of 53 excursion courses on foot, each with photo, map, and description.
The Japan National Tourism Organization provides travel guides in 13 languages. The site of Short Trips From Tokyo also seems to be nice for travelers.
Other recommendations within Tokyo and a bit further away are in the following list (still under construction; will be updated as far as possible):