Easily grow green onions. Just place the bottom of a green onion in a dish of water and set it in a sunny spot.
To regrow lettuce, cut the very bottom off so that it is smooth and place the lettuce in a container of water.
Place a stem in a glass of water. Place the glass in a sunny spot and wait for the roots to sprout. Once it has sprouted, plant in soil and water it regularly.
Carrots can be regrown from carrot tops. Just place the top of a carrot in a dish of water and set it in a sunny spot.
Celery is another vegetable that regrows well from scraps. Just put the celery base in a dish of water and set it in a sunny spot.
Regrow potatoes from potato peels by placing them in a pot of soil with the peels facing down. Keep the pot in a sunny spot, and water regularly.