If you plan to travel outside Tokyo (but in some cases you may need it also for it) more than three days and to visit at least Kyoto and Nara, you can't miss to purchase a Japan Railway Pass, that allows you to travel on pretty much all trains (including most shinkansen) at a much cheaper cost than if you bought the single tickets. There is a national rail pass which is the one that usually most tourists get, but if you plan to visit only one region (for example Kyoto, Nara and Osaka) you can get the regional one at a cheaper price. The pass can be purchased for one week or two or more weeks and it really allows you to save tons of money (they basically created it to promote tourism in Japan).
There are many agencies that sells it in the US that have all pretty much the same price (children over 12 pay as adults), we used this one, which is one of the most popular. They have a very good customer service and they ship it, together with a guide on how to use it, by FedEx very quickly -so you don't need to book it advance (also because from the moment your purchase it it is valid only 3 months), but remember that you can purchase it only outside of Japan! It is also important to keep in mind that you have to activate the pass once you arrive in Japan, and at that time you chose when you want to pass to start.
Once you have the pass, you can travel on all trains that belong to the JR system (easily recognizable by the logo) and in general you don't need a reservation. It is recommended though that you book the seats in advance for shinkansens, especially on the busy routes. You have to go to the JR office (there is one in every big stations) and they will reserve the seats for you for free, it's really convenient and fast.
When you are at the station you simply have to show the pass to the controller at the gates that lead to the platforms, and you can board any train (except the Nozomi shinkansen). Usually in the big stations every shinkanen has its one platform, so one you know which train you have to jump on, once you looked at the timetable, it's very easy to find the platform number.
We rented a car in Japan three times during our trip and I was surprised by how easy it was. Most car rentals require an International driver license, which we did here in the US with AA where it was very simple and costed only $20. You obviously have to keep in mind that in Japan they drive on the left side of the road and on the right side of the car (like in the UK) but cars are generally much smaller and very easy to drive!
We rented the car in Amami and Nagasaki with RentalCars.com (and we chose Budget both times) and the one in Tokyo with a local agency that has locations everywhere. In all three cases they had cars with English Gps (very important unless you can connect to Google maps all the time) and they provided us with numbers to call in case we were lost and couldn't communicate in Japanese. Renting cars in Japan is very popular as most people use public transportation for the everyday commute!