Taxis from Narita to Tokyo are frightfully expensive and a much better solution is to take the train. There are several choices depending on where you want to go, how fast you want to get there, and how much you want to pay.
As my hotel was situated in Asakusa, I took a train to Ueno Station, a short taxi ride away from my hotel.
At Narita Airport, the counter for Keisei (pronounced "kay say") was located just outside the meeting area for arrivals. The girl on duty explained in good English the options. The high-speed trained called the Keisei Skyliner cost Yen 1920 and it took 60 minutes to get to Ueno Station. This was a luxury train with reserved seats.
However, I opted for the Keisei Limited Express, which was more like a subway than a train. Seats were facing 90 degrees to the direction of travel, it made more stops, it took 72 minutes instead of 60, and it only cost Yen 1000, nearly half of the fare for the faster train. There were three departures per hour when I was there, but I noticed the frequency depended on the time of the day and the day of the week.
Once I had paid for the ticket, I proceeded down the escalator one floor, right into the train platform. The Keisei Limited Express is on the left, while the Keisei Skyliner is on the right. There was no special place for luggage on the former, and everyone just dragged theirs onto the train.
After numerous stops, the train got into Ueno on the dot. Once past the turnstiles, there was a ramp down to the taxi stand. If there are no taxis there, just press the button and it somehow summons taxis.