This is an experiment you need to do to believe.
Every time you are about to throw something into trash, separate out the vegetable matter and throw it into a little bin. This includes onion peels, banana peels, orange peels, apple cores, sqeezed out lemons, cantaloupe seeds, unusable ends of all vegetables, vegetables that stayed in the fridge too many days and have started to rot, peanut shells, egg shells (well, not a vegetable, in this case).
All of this can go to the compost bin instead of going to a landfill. I use a small bin that fills up every week and it sits outside my kitchen on the deck. Its one of those trash bins that is foot operated and has a removable liner container inside. This way, I can hose it off with water after it gets emptied into the compost bin.