Rubbish disposal is a very different process here. It can take on a life of its own. It is usually separated into at least three categories – burnable, non burnable and recyclable. However, each town/city has its own rules.
Here is an example of the Nagasaki city guide:
As every area handles trash separation differently please make sure to ask your predecessor or other ALTs that live in the same area as you. Some city councils will provide you with an information package that has posters (like the one above) detailing how you should separate your rubbish. Most city halls will have copies available or a printable version online.
Here is a rather detailed explanation of how and why the rubbish is sorted in this way.