Depends on when you arrive and where you are going in Shinagawa. Some of the Narita Express airport trains go right to Shinagawa Station. That would probably be the easiest. That is, unless your hotel is one that is served by the limousine bus service, which might go straight to the hotel's front door. The train is cheaper than the bus but you might have to factor in the cost of a cab from Shinagawa Station to the hotel. I prefer the train. Others swear by the bus.
I know the above sounds vague but it is hard to give specifics without knowing times and what hotel.
Train schedule:
http://www.hyperdia.com/en/
Limo-bus:
https://www.limousinebus.co.jp/en/