There are many trains and stations in Tokyo. It is very complicated even for Japanese. So many people use applications for Route Search.
There is also an English version. You just put your departure time or arrival time, so you can know the shortest route and which train you should take.
Most of prepaid IC cards can be used not only for transportation, but also for shopping in convenience stores. It is very useful. If you stay in Japan for long, we highly recommend that you get one.
There are some prepaid IC cards. SUICA is by JR East, and PASMO is good for some trains and buses. You can choose it according to which transportation you use more daily.
You can buy SUICA in JR stations. But, only in limited machines. You can ask the staff there. For PASMO, you can buy them over the counters in the stations associated.
Same as in the Philippines. You can stop a taxi by raising your hand. Tell the driver your destination.
Fare depends on the areas. In Tokyo, 410 yen for the first ride. 80 yen is added every 237 meters.
From 10PM to 5AM, fare will be increased by 20%. Taxi fare will be very expensive compared with public transportations.
To get to Narita airport, you should take a train or bus.
From JR Ueno station, you can take Skyliner. From Shinagawa, Shibuya, Shinjuku and Ikebukuro, you can take Narita Express.
These are express trains. (Strongly recommend express trains because conventional lines take much time.) Direct buses to Narita Airport depart from many places in Tokyo.
Please check the website below for more info.