Due to business reason, I travelled to Kawasaki, Japan lately.
Here are some tips travelling around. Firstly, here is the site name to check out detailed schedule of trains around Tokyo.
Secondly, the fastest way from Narita Airport to Tokyo is by Narita Express. Narita Express will start from Narita Airport Terminal 1, pick up more passengers from Narita Airport Terminal 2 & then go straight to Tokyo with no stop in between. Ticket price is about 3000+ Yen. There is 1 such Express train about every 30 minutes. So check your flight schedule & train schedule in detail. I managed to come out of the arrival hall, buy a ticket from the booth which is right in front of the arrival hall & boarded the Narita Express in 15 minutes. Note also, ticket for Narita Express is specific to the exact batch of the train. The counter told me, if I miss the particular train, I can go back to the counter & they can change it to the next available one. The trip from Narita Airport to Tokyo is about 63 minutes.
There are other cheaper alternatives taking normal JR trains. These trains stop over at other train stations between Narita & Tokyp & take about 1 hr & 30 minutes to reach Tokyo. If time is not a concern, you can check out the site above. Usually it will show you the alternative routes in details.
At Tokyo Eki(station), before you come out from the station, what you can do is to go to the counter & show them your narita express ticket & tell them you want to change to a JR ticket to say, Kawasaki. And the counter will issue you another ticket. For Kawasaki, I have to take the Tokaido line towards Yokohama & Ofuna.
I supposed it is possible to go to the JR counter at Narita Airport and tell them you want a ticket from Narita Airport to Kawasaki taking Narita Express. I did something like that on my return trip from Kawasaki to Narita Airport. The counter should issued me 2 tickets, 1 from Kawaki to Narita Airport & another Narita Express ticket from Tokyo to Narita Airport.
Lastly, for business travellers who claim transport allowance, you will want to keep the train ticket. Before you exit from any train station. You can just tell the security that you want to keep the tickets, they will put a stamp on your ticket & you can pass through the gate without using the ticket.