It looks like there are some pretty great Tokyo subway maps out there (I love maps, had to look). That's one of the most complex I've ever seen. It looks like there are several different options - I found some English maps, I'm sure someone out there has a recommended route from which ever way you are coming in. I'd say that's probably your best bet. Shame those direct buses only seem to go in the mornings.
The Narita Express train is the easiest route from the airport, and costs about $25, and will go to whichever the most appropriate major train station is in the city (usually Tokyo or Shinjuku). From there you can transfer to the subway. From anywhere in the city getting to Disney is easy and via the same route - take the subway to Tokyo station, then the Keiyo line to Maihama. The train line goes as close to the park as the monorail does at Magic Kingdom, so you can't miss it!
One year I was staying right in the middle of the city, miles away from Disney, but still managed to get up early, take the train, and be at DisneySea an hour before park opening, so for the budget conscious it's not the end of the world if you can't stay close by.
Trains and subways shut late at night (hence Tokyo Disney always closing promptly) so a late arrival will need a shared ride or town car, but there are always lots of people at the airport offering rides and assistance, and you will be on a flight with many other people, all of whom want to go to the same place, so it's not hard to pool resources and share ride fares to get into the city.
One thing I think lots of foreigners don't realise is how - despite language and culture issues - the politeness, friendliness and lack of any crime makes a tourist feel far safer and more relaxed than in many American cities, and you can soon find your way around, even if it can be initially confusing.
Finally don't worry about the long flight time - chances are the lines for the Epcot version will be even longer than the flight!
