Narita airport is 40 miles (70km) away from Tokyo.
So don’t think about taking a taxi: it would be horribly expensive (there is a fixed-price taxi service: over £80 -depending on where you’re going).
The options really are train, or the “airport limousine bus”.
Good if you haven’t got much luggage. The JR Narita Express (NEX) train goes from the underground stations at Terminal 1 or 2 of the airport. You need to go to the NEX counter in the airport terminal first, to reserve a seat. The train journey to Tokyo Station takes about 50 minutes, and costs about Yen 3,000 (£18)*. The JR Airport Skyliner train gets you to Tokyo Station in about 80 minutes. No seat reservation needed. It costs around Yen 1,300 (£7.60)*. * The Japan Rail Pass covers the NEX and JR Airport Liner trains. So if you have bought a Japan Rail Pass before arriving in Japan, you can travel on these trains for free! Just validate your Japan Rail Pass Exchange Order at the JR Service Center at the airport before getting the train. (Seat reservation still needed for the NEX.)
Airport limousine bus:
Good if you have quite a lot of luggage, or want to go directly to a hotel. Go to the Airport limousine bus counter in Terminals 1 or 2 to get information and tickets. The main destination is Tokyo City Air Terminal (TCAT), but there are other services which drop off at various hotels in Tokyo. Journey time about 1 hour, price around Yen 3,000 (£18.00)*.
* Approximate conversion using Yen 170 = £