For Tokyoites, garbage is a rather constant preoccupation. This is not only because there are strict rules for separating trash but also because you can only put trash out on certain days. A lot of people also have experience with "trash Nazis" who police how trash is sorted and hassle those who make mistakes.
All of the sorting and holding back of various sorts of trash until the appropriate day arrives for removal wouldn't be such a big deal if homes weren't so small. There really isn't any place to keep trash temporarily other than in your home for most people and the smell can became a problem, particularly in summer when it's hot and humid as all get out.
My own solution for this is to make sure I wash out anything nonburnable (such as plastic containers) with food residue in it and to separate food scraps into a separate sealed pail which I keep under the sink. If you keep the types of things which may rot separated and sealed off, the smell is contained.
I've discussed this with a few of my students and they've told me some things which explain certain behaviors in supermarkets. For one, there are spools of very thin plastic bags at all markets. These bags are on the smallish size and I always thought they were for putting possibly leaky trays of meat or fruit and vegetables into. However, I see women grabbing hold of the spool and tearing off a good many of them and stuffing them into their shopping bags. Since the bags are thin and small, I never understood what women wanted so many of them for but my students told me they were for putting food scraps into and then sealing them up so they didn't stink up the trash.
One of my students told me she goes a step further in this regard. She can't bear the notion of there being any food scraps rotting in her trash, even inside of sealed bags. She actually stores the food in the bags, seals them, and then keeps them in her freezer until trash day when she takes them out and tosses them in the bin. I told her that I had no space in my freezer for this sort of thing and she said she didn't either but she crams the scraps in there regardless. Personally, I'm not so sure that food scraps in my freezer with my still edible food makes me feel any better than having them in the the trash where they'll decay for a few days before the trash goes out.
It is important in Tokyo to try and reduce the smell of your trash as much as possible though as it will attract roaches (and other unpleasant creatures). It's a good idea to wash your trash cans out regularly with baking soda and plenty of hot water and soap. It's also important to change the liners each time you toss the trash even if they seem relatively clean. It's also important to give recyclable items a thorough cleaning (particularly beer cans) so that they don't start to smell up things and attract unwanted guests.