Japan: Shinkansen

The shinkansen is probably the most famous train in Japan and when thinking about Japan, shinkansen will be one of the first things to come to mind.
It's also the fastest and most comfortable way to travel around Japan. It's probably also the most expensive one but the train is always on time.
Getting a ticket is a bit tricky which is mostly because train staff do not speak very good English, if they speak at all. I therefore recommend you come prepared and have the travel information with you so you only have to point.

Basically, the shinkansen covers all major lines throughout Japan from Fukuoka in the southwest to Sapporo in the north east. Along the main line between Osaka and Tokyo, shinkansen departs every other minute.
There are also different kinds of shinkansen and operation lines are split into different regions (i.e. JRWest, JREast) so googling the information is a bit tricky sometimes. Again, if you want to have information about departures, I recommend Hyperdia as it provides you with everything you need to know.

When you buy a ticket, you always buy that ticket for a specific train on a specific date. You buy a ticket for a train, you are bound to use that and only that. There are special ticket gates for the shinkansen and you use it just like any other ticket gate.

Usually when buying a ticket for the shinkansen or another limited express train (there are a few but apps like Hyperdia will tell you that) you also need a seat reservation. There are specific waggons without reservation but they are rare and it's much more comfortable that way.
If you travel long distances as a tourist, you might want to check the JR pass as you can use some types of shinkansen with it as well without having to reserve a seat. But the pass is really expensive so unless you plan on using the shinkansen all the way from Fukuoka to Sapporo, it hardly ever checks out.
But again, using apps like Hyperdia will help you plan your trips and your calculations.

When buying a ticket, you can do so either through a vending machine or the ticket office. As mentioned above, the staff in Japan is usually not very fluent in English, so better provide all your information written down so it's easier for them.
If you already know which trains to take, JREast also offers online reservation:
http://www.eki-net.com/pc/jreast-shinkansen-reservation/English/wb/common/Menu/Menu.aspx