Japan Travel Fixes
I don't know how to dispose of trash at the hotel or on the street
Your hotel room's trash can can usually just be used as-is. Public trash cans are rare on the street, so the norm is to carry your trash with you, or use a convenience store bin for things you bought there.
Japan's sorting rules are detailed and vary by municipality, but for what you generate in your hotel room, most properties are fine with it all going in one bin, unsorted.
Public trash cans are scarce partly due to a history of removal for security and cleanliness reasons — carrying a small bag with you is a handy habit.