Best way to get to Central Tokyo from Narita airport.

Firstable,  confirm your airport Narita or Haneda.
If it is Haneda, transportation is very reasonable and fast. No-problem.

From Narita to Haneda, there are several ways to get to City Central.

1, Bus
  1-1, Limousine Bus
  1-2, Other Bus
2, Train
  1-1, JR Narita Express
  1-2, JR Rapid
  1-3, Keisei-Sky-Liner
  1-4, Keisei-Access express (no express charge)

Generally, more expensive - faster.

But, If you want to go to Tokyo sta. or Ginza area,
Best way is to get Bus to there.

Limo-Bus needs over 3000 yen, but 2 Bus services offer 1000 yen access.
Don't take Limo-bus when your destination is Tokyo sta. or Ginza.

1, Access Narita  http://accessnarita.jp/en/home/
2, Narita shuttle  http://www.keiseibus.co.jp/en/kousoku/nrt16.html

Just one hour and 1000 yen. These are the best way. No doubt.

For (1)Access Narita, you don't need to buy the ticket.
Only you need to line at bus stop and pay to driver.

For (2)Narita shuttle, you need to buy tickets at counter inside terminal.

I say again. Don't take Limo-bus to Tokyo sta. or Ginza area.
Enjoy your stay in Tokyo.