I arrive at Narita International T3 at 19:00. I need to get to accommodation in Shibuya.
Quickest and easiest might be conflicting here unfortunately. The Tokyo subway system is complex. You have two main options:
Arriving at 19:00 you probably won't make the 19:50 N'EX, so the next one, leaving Narita T2/T3 station at 20:47 would be the one. Arrive at Shinagawa at 21:52. Change to the Yamanote line. Five stations to Shibuya. A train every 5 minutes or so.
Keisei Skyliner, leaves Narita T2/T3 (railway) at 20:12, arrives 20:48 at Nippori. Change to Yamanote line, 13 stations to Shibuya, arrives 21:26.
The easiest way it to catch a taxi. They are available at the airport, and will take you door-to-door. The catch is that Narita is a long way from Shibuya, so the taxi fare will be very expensive. At that time of night, taxi may also be the quickest option (although it will depend on the day of the week and some other factors).
The two cheaper (although not necessarily cheap!) options are Airport Limousine Bus , or the train.
The Limousine Bus has the advantage that it will often be able to take you door-to-door, as it goes to many of the popular hotels, including several in Shibuya. Schedules and routes are on their website.
There are several options for the train, with the main two being Narita Express (NEX) or the Keisei Skyliner - although the latter will require at least one change of train to get to Shibuya. You can use the HyperDia website to get options/prices/etc depending on your exact departure time/date.