Traveling around Tokyo

So what would be the cheapest way to travel all around in Tokyo? I'm getting a little confused reading things and i need some clarification. If you could help me, it would be much appreciated. Thanks ^^

One reply can be: One of the longest ( 1 hour ) and cheapest rides around inner Tokyo is to board the JR Yamanote line at Tokyo station, to go around the whole loop and to disembark one station after Tokyo, either Kanda or Yurakucho, what is Yen 130 total. But this means you may not go through the ticket gates at any of the stations on your way.
The other reply can be: There are various means of transport within Tokyo: JR trains, private trains, two subway companies, a streetcar, buses, other lines ( Yurikamome, Rinkai, Monorail and so on ) that is depends on where you want to go. There is no all inclusive day pass for ALL means of transport, but there are different passes for most travel needs. See this japan-guide under Tokyo travel : http://www.japan-guide.com/e/e2017.html

Most of the places like Shibuya, shinjuku, Harajuku, Ueno are on the JR Yamanote line.

There are a few like Asakusa that would require transfer to the subway line.

To plan your trip you can do the following:
Check out which station your destination is closest to, and next check out which train line it lies on.

Best way to see which trains to take is via http://www.hyperdia.com

only bad thing about the site is you need to know the exact spelling of the station.

First, I recommend getting the Kodansha 'Tokyo City Atlas, A Bilingual Guide'...it is not too big, it's got subway & train maps, index of hotels & attractions, buildings by name, it's just a good book to have in Tokyo. It's not a guide book, though...nary a word of advice. It's just a very very good map book.
Second, how you get around Tokyo depends on how much you are into counting your pennies. If a few hundred yen are important to you, then follow somebody else's advice. If convenience is important to you, then get a PASMO or SUICA card and ride around wherever you want without thinking about it. There is no discount; they are just stored-value; but the issue is convenience.
I use PASMO because I am on the Keikyu line (a non-JR line outside Tokyo) and it works like this: go to any ticket machine with a pink PASMO symbol, and buy the card. You have to put in a deposit of 500 yen, and then everything else is just money to be used on JR, private lines, vending machines that say PASMO, convenience stores that say PASMO....no calculating. No waiting in line to buy a ticket (which always seems to be the case at Harajuku when I am there). The downside is that you might overestimate and put too much money on the card; I have never turned one back in, so I don't know how it works - you'd think you'd get the 500 yen back, but no doubt somebody in this forum knows.
I hate standing in line at stations...at the line to buy tickets, at the fare adjustment line, whatever...so I keep a PASMO loaded up and don't think about it. I can hop from line to line, who cares. That leaves me free to just think about where exactly I am going.
I haven't bought SUICA but I can only assume they are similar if not the same.
I think Tokyo transportation is cheap. I don't think it's worth being on vacation and buying individual tickets for each ride. I'd put 1000 yen on a PASMO and go from there.