There are two major airports in Greater Tokyo metropolitan area. Narita and Haneda airports. Narita airport is connected by JR and Keisei lines. Japan Rail Pass holders can take limited express Narita express to Tokyo and other major stations in Tokyo. For non-Japan Rail Pass holder, taking Keisei line can be cheaper and faster way to reach downtown Tokyo.
Haneda airport is connected by Tokyo monorail and Keikyu line. Tokyo monorail is running between the airport and Hamamatsu-cho station on JR Yamanote loop line. Hamamatsu-cho station is close to Daimon station which Toei Asakusa and Oedo subway lines are running. Keikyu line is connecting Haneda airport and Keikyu-Kamata but most of the trains run to Shinagawa station which you can change to Yamanote loop line. The trains are also continue to run on Toei Asakusa line.
Due to there is no JR line connecting Haneda airport, Japan Rail Pass holders think that they have to buy the ticket to leave from the airport. However, Tokyo monorail is a subsidiary of JR East which means you can use the Japan Rail Pass on Tokyo monorail!
There is a Japan Rail Pass exchange office at the arrival hall. Even if you want to start using the pass later, better to exchange here due to staffs at Haneda airport speak English better than other stations in downtown Tokyo.