We used a travel agent to book our flights on Delta, although if you are doing a simple in/out of Tokyo, you can probably book on your own (also, it is a long-ass flight, and I use the word "ass" purposely, as in, it will be numb at the end of 12 hours or so)(your mileage may vary).
We also bought Japan Rail Passes, which may or may not save you some money but more than makes up for any not-so-great-deal in convenience. You can get these through a travel agent, but it's super easy to do it yourself online at a number of sites, including jrpass.com (which is what we used). You must do this prior to traveling! The pass is available in Japan at times for a limited time period, but these deals seem to come and go, with expiration dates.
You will receive a JR Pass voucher - not the actual pass - which then has to be redeemed at a JR Travel Center - so allow some time to do this when you arrive.
The JR app is, for some unknown reason, called Hyperdia and Hyperdia Voice. You can get a free trial (30 days I think), otherwise it's about $3. And it's a great app. Advice - go into the app settings and make sure you turn off the air travel option (unless, of course, you plan to travel within Japan by air!). Also, make sure you turn ON the Japan Rail Pass Search option, which will restrict your searches to routes that accept the pass (some local trains, and two shinkansen lines, don't).
We screen-shot (is that a word?) several schedules for each travel day, in case we had no wifi. In addition to times and train names/numbers, you can see if you have to reserve a seat (mostly, no), what platform the train leaves from, trip duration, train transfers and more.
Also. shinkansen. 200 mph hour, man. We were able to cover a lot of ground because of the bullet train.
If you are going to Tokyo, I cannot say enough great things about the Tokyo Metro app, simply called TokyoSubway.
Also, the subway system is SIMPLE. Color-coded, stops are numbered, signage in the station indicates exactly which direction trains are going in. Inside, most of the trains have displays showing where you are, where you are going, and there are announcements for each stop in English. Ticket machines have an English option. The whole thing is awesome. Also, CLEAN. If you like your subways with trash, bad smells and graffiti, you'll be disappointed.
Google Maps also works, although in some cities the public transportation options do not show up. We used Google quite a bit to find the walking routes between places, using just GPS (open the map while connected, plug in your directions, then refer back to it as you go).
Things to look for at stations: tourist information offices, usually well-marked, usually have some English-speakers. Exit signs list major tourist attractions and even hotels to help you find the right exit out of the train or subway station (NYC could really get some lessons here).
We used several taxis in Kyoto, where the public transportation is not very comprehensive. I would not hesitate to recommend them as a more efficient way to get places, and the prices were not outrageous. Most drivers have a little English, but it helps to have a map, or a card from your hotel, or a note in Japanese (provided by the hotel). Buses can be a little confusing, but aren't a bad option at all. You'll need exact change (it's a great way to get rid of all the 10 yen coins you'll end up with), usually 200 yen per ride. Many cities have tourist loop buses that are hop on/off at the major sites, and offer single or multi-day passes.
WALKING. You will do many miles of it. Break in your good walking shoes before you leave.