InsaneJournal

It is a fabulous webpage. It is one of those very few where it becomes fun to play with. Enter any Tokyo {and by Tokyo, I mean the entire area from Narita Airport to Miura-shi} subway or train stops, change the time of day, and see what it returns. (Did it find a zero transfer ride? Did it put you on a limited express train? Where is the station where you have to transfer? [You can click on a map link to see the area.])

The website's importance to you, the English-speaker contemplating a trip to Tokyo, is that is it gets you out of the grip of the Japanese Railways system [i.e.: the JR lines].
Please interpret this correctly. The JR lines are good, and there are situations and locations where they will be the least-costly, or the most rapid route, to your intended destination.

But where JR seems to make a good deal of its profit is by placing its overseas, English-speaking customers, in train bondage.
It wants to sell you a JR-only train pass before you ever touch down at Narita. Its price for it will put the kernel in your mind, "In order to get the value from this pass, I should ride JR lines exclusively.".
Further, I have ridden the JR lines enough to realize that, even on the Yamanote line, which should count for a 14th Tokyo subway route {although the 13th route, the Fukutoshin line, will not open until June}; the in-car electronic display denoting your route and the next station, as well as the Japanese and English-language recordings, does not inform you when you can transfer to a non-JR route. But when you ride on a non-JR route, including the Tokyo subway, as well as the non-JR private railways, all will tell you when you can change to a JR line.

So the Hyperdia website [Hitachi Information Systems is behind it.] takes the ropes of the JR lines off you (if you will). It lets you know that you do not have to rely on JR getting you from central Tokyo to Yokohama [for example]. You'll discover that it is possible to take a train which will provide a one-seat ride between the two cities, which won't involve you having to navigate the mixing bowl of Tokyo station, and which will cost you less money.

Once you start playing with the Hyperdia website, you start noticing the little annoyances which reside in its software. The route and fare calculator seems to have as its prime directive getting you from point "A" to point "B" in as rapid a time as possible.
The website does not let you specify that the lowest cost, or the fewest amount of transfers, is your prime directive.
But you can work around this. Unfortunately, it involves you having some knowledge of the Tokyo subway system. You should download this .pdf of the Tokyo Metro Guide [right-click and select "Save Link Target As..."], or open the Wikipedia entry for the Tokyo subway in another tab.

I am going to use the "ASAKUSA(TOBU)" [station names are in all caps by its software] station as the example because it is the stop nearest the hostel where I stay in Tokyo, and its stations are served by the

1. Toei
2. Keisei
3. Keikyu
4. Tokyo Metro
5. Tobu

To avoid these inconsiderate transfers, you have to nudge the software and use its intermediate stations feature. For that, you need the print guide of stations. To ensure that you stay on the Toei Asakusa line, include a name of another station on the Toei Asakusa line between SHIMBASHI and ASAKUSA(TOBU).

With this knowledge, you should be able to sidestep the software's attempt to route you over multiple companies' routes unnecessarily on all the Tokyo subway lines.

The other niggling snag with the software is how it breaks down through-routed trains into segments, and obscures that this particular train originates or terminates at a station beyond the range of a specific mid-route station. (How do you find out that this is a through-routed train? Click on the graphics of a subway train just to the right of the timetable clock. Notice that the train number remains the same.)
When will you be exposed to this? Probably on your first route exploration - from Narita Airport to wherever is your hotel / hostel destination (if you are keen enough to ride the Keisei Limited Express train [not the premium fare Skyliner], which you should).
Your arrival at Narita is where you will find good transit passes on offer. They are not for the JR lines.

You will need to exchange some money at Narita. There are multiple banks offering currency exchange services on each floor of either terminal at Narita. They will probably all have the same rates. Do not change a lot of your funds there. [This small corporation, which I know has branches in Ueno & Shinjuku, advertises that it betters everybody else's rate by some percentage.]
But you do need cash for this special ¥980 two-day open ticket from Tokyo Metro. As that website informs you, it is available only from one ticket counter in each terminal: That of the Keisei Rail line. The wacky aspect is that you obtain this Tokyo Metro pass at this counter [realize you cannot use this pass to get from Narita to Tokyo], but not the ticket you will need to get from Narita to the ASAKUSA(TOBU) subway station. I also alert you that this two-day open ticket is valid only on the eight Tokyo Metro lines - not the four Toei lines.
To get back to the broken-down segments of through-routed trains; The software likes to consider a two-station portion (The AOTO and KEISEITAKASAGO stations.) of the Keisei Main Line as a separate route. Every train on the Keisei line serves these two stations. It is not as though this is a shuttle line which you must ride to get from one area of the service to the other. An inbound train serving these stations will go on to one of three destinations. An outbound train serving these stations will go on to one of four destinations, unless it terminates at KEISEITAKASAGO. This software feature masks which trains are going on to, or eminating from, the Toei Asakusa line. (Again; click on the subway car graphic and note the train number.)

If your hotel / hostel in Tokyo is not in Ueno, you will have to transfer to another Toei Asakusa line train at the AOTO station. It is an easy across-the-platform transfer. Wikipedia reports that there are six trains every (18-hour) day which migrate from the Keisei line directly onto the Toei Asakusa line via the Oshiage line, but you should not expect to catch one of those trains. (If your hotel / hostel is in Ueno, you should disregard everything I scrawl here about a Transfer Ticket. You want the regular Keisei Limited Express train from Narita to KEISEIUENO. That costs ¥1,000.) Say you got a good deal in Shinagawa or Shinjuku. Use the Hyperdia site to compute how much it will cost to get to Shinagawa or Shinjuku. If you are staying in Shinagawa, you will not have to transfer a second time. (Do not board an Asakusa line train destined for NISHIMAGOME.) If you are staying in Shinjuku, you will have to transfer once more to a Toei Shinjuku line train at HIGASHINIHOMBASHI. {There are hyphens in the station names after the second "I", but the Hyperdia software discards all hyphens in station names.}

You will purchase your train ticket to Tokyo from the automatic machine in the Keisei station in the basement of the terminal.
After you switch the machine's language to English; the button you need to hit is the one labelled "TRANSFER TICKET". The Keisei route which accesses the Tokyo subway system is the "OSHIAGE LINE". Hit that button.
The next screen after you indicate the Oshiage line will have an array of buttons with fares indicated. In my instance, the fare to ASAKUSA(TOBU) is ¥1,060.

The exposure to the Keisei line at Narita is the clarion call that there are other private railway corporations (besides the JR) serving Tokyo. These other railways seemingly have a non-committed attitude with English-speaking travelers. It is as though the corporate viewpoint is, "Japanese-speaking commuters are our main customers, and where we direct our marketing. Any other travelers are a bonus for us."
So we have to unpeel another layer to learn where they run.

But in this instance, I shall denude the entire Tokyo metropolitan area for you here and now. This is Jacek Wesolowski's bilingual [English / Polish {!}] illustration of the comprehensive and actual Tokyo subway system. It blows off the lid of what you or I considered it to be. The line to Narita Airport, at approximately 60 km from central Tokyo, is the farthest it extends. But look at how far the lines go in the other compass directions. If you downloaded the .pdf of the Tokyo Metro Guide, refer to it again. Note what it does not show you, but obscures in the small print accompanying a faded subway line color extending off the edge of the guide.

If you opened up another tab for Wikipedia's 'Tokyo_subway' rubric above; use it as a hub as you click through to each of the train lines to which it links. You will be informed as to which subway lines have reciprocal operating rights over which private railway lines. (You will even find the one subway line which actually operates on JR trackage.) When the Fukutoshin line opens in June, it will have reciprocal service from HANNO and KAWAGOESHI to SHIBUYA.
This is the page from which's link I found J. Wesolowski's illustration.

Where is SHINRINKOEN [the diminished yellow line leading away from the Waköshi terminus on the Yürakuchö Line in the upper left corner]? If you have Shobunsha's Tokyo Metropolitan Atlas [ISBN 4-398-20103-3], Shinrin-köen (in Saitama) is in there only in the 'road map' portion of it. We would have to buy another atlas to get the street layout of Shinrin-köen. It is that far off the beaten path. But it has direct service to the Tokyo subway.
Would you like to visit Shinrin-köen the next time you explore Tokyo? Use Hyperdia to discern your route and your cost. You would probably be the first gaijin its residents have seen since 2002.

There are so many other areas which the Tokyo Metro Guide merely name-drops, and in which the Tokyo Metropolitan Atlas only imparts the train station names; and because these city and station names are complete mysteries to us, we have not caught on.
May this weblog entry blow off the lid of the non-touristed sections of Tokyo and encourage you to go there without paying an emperor's ransom to the JR. The next time I go onto the inbound platform of the Toei Asakusa line's ASAKUSA(TOBU) station, I will board that Limited Express to MISAKIGUCHI and not exit in Yokohama this time. I wonder what will be there.