Narita International Airport: For Narita city—not Tokyo—take the Keisei Main Line to Keisei Narita: about 10 minutes, roughly ¥250, with frequent departures. Do not board trains marked “Narita Sky Access Line”/Access Route; they head toward the airport–Tokyo corridor rather than Narita town. JR Narita is a short walk from Keisei Narita. A taxi direct to town is about ¥3,500, so it only makes sense with heavy luggage or a group.
Tokyo Station: Take the hourly JR Airport Narita commuter service on the Sōbu Line to JR Narita: about 75 minutes, roughly ¥1,110. It is the simple choice from central Tokyo and is covered by the Japan Rail Pass. Do not pay for the Narita Express unless its limited peak-direction stops happen to suit your timetable.
Keisei Ueno / Nippori: Keisei Main Line commuter trains run to Keisei Narita in about 60 minutes for roughly ¥810. This is usually the better-value Tokyo-to-Narita-town route. Avoid Sky Access/Access Route services: they are designed for Narita Airport, not Keisei Narita station.