In Japan, travel is pretty simple and safe. Even if you don't read Japanese, you can get where you want to go.
On my first day, I traveled from my town to Nagoya by local train. A great English website I use all the time is Hyperdia. (It's also available in Japanese and Chinese). It will give you all the options - types of train, reserved seat or not, fare cost, times, places to transfer, etc.
This is a real policeman at the Nagoya Station.
When I got to the Nagoya Station, I transfered to the subway to go to the Nagoya Castle and rode on the "Women Only" car. They don't have men only cars. Not yet anyway.
After visiting the castle, I took the subway back to the Nagoya Station, then the train to the airport. I booked my plane reservation on the internet, using the JetStar website. JetStar is one of the low cost carriers. The basic fare is very cheap, but you have to pay extra if you want to check luggage or choose your seat, which I don't. You are allowed 7 kilograms of carry on. I pack light and had almost five when I left home. I wanted to give myself some allowance in case I purchased something to bring back from my trip and still be under seven on the way home.
I took a bus from the airport to the area where my hotel was located in Kagoshima and was able to find the bus schedule online in English ahead of time.
In the morning I walked from my hotel to the port to get the ferry to Yakushima. The ferry schedule is online in English and runs once a day in each direction - 8:30 am to Yakushima, 1:30 pm back to Kagoshima, so don't be late! The ferry carries people as well as vehicles and on board had several small places selling food, machines selling drinks, and a manga library where you could borrow books.
On Yakushima, I rode the bus to and from the place where I hiked. Multi day bus passes are available, but I was only traveling one place and back by bus, so I didn't buy one.
I took the ferry back to Kagoshima from Yakushima. The Shinkansen (bullet train) was how I traveled from Kagoshima to Kumamoto, a little expensive, but very fast.
The next day, I took a bus from Kumamoto Station to the port where I caught the ferry to Shimabara. It was rainy that day, so I didn't take any ferry pictures. From the Shimabara port, I took the bus to close by the Shimabara Castle. After visiting the castle, I walked a couple of blocks to the train station, where I caught this "one man" train and went to Nagasaki.
In Nagasaki, I rode a tram a couple of times to get around the city.
I took the highway bus from Nagasaki to Fukuoka. You have to make a reservation ahead of time and you are assigned a seat for the bus.
In Fukuoka, I took the subway to go to Ohori Park, but most of the other places I visited were close enough to walk from my hotel. I also took the subway to the airport. I flew from Fukuoka to Nagoya.
The train from the airport to the Nagoya Station shows the speed and the view from the front of the train.
I took the train home from Nagoya. I really had a great vacation!