Nihombashi station map in Japansese

You will arrive at A13 platform 1 at lower right and need to get to T10 in the middle. You will exit Toei Asakusa line part of the station, descend one level and enter Tokyo Metro's part.

Best thing to do is to buy an IC card at Narita airport station, then you don't need to worry about looking up fare and buying transfer tickets. JR East sells Suica whereas Keisei and the subways sell PASMO.