I was asked last time by someone to show the way to go to the city (Chiba or Tokyo) from Narita Airport. Taking the train in Japan is fairly easy because there is lots of English signs almost everywhere. The ticket machine also has the english version so you will not have any trouble purchasing the train ticket.
The train station is located inside the airport. Once you reach the place, you will see two ticket gates. The first gate is for Keisei line.
The Keisei Line is bound towards Nippori, Ueno, Nihombashi, Higashi Ginza, and the Keikyuu line. Unless you plan to go there, don't take the Keisei Line.
The second gate is for JR line. Sorry for the blurry photos. I was holding it with one hand and forgot to change the setting. >_>
The JR Line goes toward Tokyo, Shinjuku, Ikebukuro, Yokohama, Ofuna, and Chiba. Inside this line, there are basically three types of train. Narita Express, Rapid, and Local. For Narita Express, you need to purchase a special ticket on the counter before you enter the gate. There was no significant difference between the trains for me, so I pick the local one which was the one available at that time.
While in the train, there is a rule to silent (or change it to manner mode) your phone. You will hear this announcement in the train every time. It is also considered rude to talk on the phone inside the train. But nowadays it is pretty normal to see people talk on the phone inside the train.
It's normal to see lots of advertisement in the train with yummy looking girls on it. ^^
At the end, there are usually priority seat for... priority people. Around that area, you are supposed to turn off your phone. I think nobody does it though.
If you already inside the train, just sit down, relax, and wait until you arrive at your destination. You might need to change train depends on your final destination.