If you are a resident of Japan, throwing away your household garbage at a convenience store is somewhat scorned. You may ask, "why use a convenience store?". Many wards and cities in Tokyo require that you purchase special garbage bags for your household trash, with a large bag running about 100 yen. To get around paying for this, many will simply take their garbage to the convenience store to throw it away at no cost.
If you are a traveler, you shouldn't have to worry about buying special bags for your garbage, and you don't need to be concerned about throwing away the day's trash at a convenience store, but you still should be aware of the separation between different trashcans. Burnable and unburnable are the basic categories, but there is in some cases another can for plastic. Cans and bottles always need to be recycled, and this should be easy enought to follow.
You may have trouble finding regular trashcans around town, but you will always be able to find recycling bins for cans and bottles. Please use them, as you really have no excuse not to!