Hi there!
Tokyo is serviced by many rail companies, but by far the most useful are the JR rail network around Tokyo, and the non-JR Metro system.
You should purchase the [Narita Express and Suica prepaid deal] from Narita which will give you discounted travel into Tokyo, and also a prepaid card charged with ¥1500 that can be used on both the JR rail network and the Tokyo Metro system.
To get to Tokyo Tower from Narita get the Narita Express into Tokyo Station, and then use the JR Yamanote line to Hamamatsucho for Tokyo Tower. You can find out more information on Tokyo Tower access here.
From Tokyo Tower/Hamamatsucho, you can get the JR Yamanote line again to take you to Shibuya. The cost for which will be around ¥190.
By the way, if you like towers - you should also try and pay a visit to the new Tokyo Sky Tree while you are in Tokyo. This is the worlds largest free standing tower so you're sure to have a good view (As long as there are no clouds!). Here is more information on how to get there - with a Suica prepaid card you should use the Metro to get to Asakusa and then use the Sky Tree line to get to the Sky Tree Station, or stay on the Metro to Oshiage metro stop and walk from there (I'm sure you'll be able to see it ;) ).
You can look up train timetables and costs for all of your legs at the Hyperdia travel planning website.
Hope this helps and you have a great time!