By plane
From Narita Airport, the fastest and most expensive way to reach Yokosuka is to take the Narita Express to Shinagawa, and then take the Keikyu Line to the centrally-located Yokosuka-Chuo station. (2 hours; �3930 [�3310 JR fare + �620 Keikyu fare]). With the Japan Rail Pass this trip costs only �620 for the Keikyu line.
Regular JR commuter trains depart Narita Airport once per hour: some trains offer one-seat rides to JR Yokosuka station, or else change at wherever the train terminates to the next train bound for Yokosuka or Kurihama (About 2 3/4 hours, �2520). These trains offer a �950 Green Car seating upgrade; Green cars feature more comfortable seats and a drink and snack service.
A cheaper ride from Narita to Yokosuka is to take the Narita Sky Access train which runs into the subway. When you reach Sengakuji, change to a Keikyu Limited Express train for Yokosuka-Chuo (2 1/2 hours, �2020).
From Haneda Airport, take any Keikyu Line local or express train and change at Keikyu-Kamata station to a limited express towards Yokohama. The trip to Yokosuka-Chuo takes 50-60 minutes and costs �790.
By train
The fastest Keikyu trains (the Limited Express "green trains" - referring to the color of the sign on the train, not of the train itself) make the run to Yokosuka-Chuo in 43 minutes from Shinagawa station (�620). Many trains from the Toei Asakusa subway line continue on to the Keikyu Line. The ride takes about one hour from Nihombashi station (�900).
The slower JR Yokosuka Line, on the lower level of Tokyo Station, takes you to JR Yokosuka Station (75 minutes; �1050) which is about 2 1/2 kilometers northwest of the more centrally-located Yokosuka-Chuo Keikyu station. If you wish to use JR, be sure to take any train bound for Yokosuka or Kurihama (and note that the front 4 cars of the train are removed at Zushi when Yokosuka-bound, so ask if you are not sure where to sit).
Local buses