First off, check out what I grew from bits of a green onion I was about to toss out!
It's so easy anyone can do it. Start by buying a bunch of green onions (spring onions, scallions) from the store. They can be organic or not, which ever you prefer. The ones shown here are grown from ones I bought from Walmart for a quarter.
Lop off the bottoms, leaving about 2-2.5 inches of the white part, along with the little roots. Use the tops/greens. Plunk the roots in some water, making sure just the roots and a little bit are submerged and place it somewhere in the kitchen. Now watch how much it'll grow in a day or two! Change the water every couple days. Once the roots are a few inches long, transplant them in a deep pot (8+ inches in depth is good) with potting soil/compost or into the garden bed about an inch apart. Bury most of the onion, but leave half an inch of the top above the soil. Keep it well watered and fertilized. That's all! Just snip some off whenever you need it. Enjoy!
There are lots of other things you can grow from scraps!
P.S. You could just leave them to grow in a glass of water, but without all the nutrients and goodies from soil and compost, over time the greens will loose their flavour and become unworthy of eating. I highly suggest you transplant them!