Like growing green onions, growing celery from leftovers is also fairly straightforward. When you chop up the celery, leave the base of the plant in tact. Sit the celery base in water (like you did with your green onions) and leave it in the water for about a week. Mary and Tim of the blog 17 Apart tried growing celery this way and recommend changing the water every couple days.
After a week or so, you will notice small, yellow leaves growing from the middle of the plant and the outer stalks will start to deteriorate. At this point, you can plant your celery in soil, either in a pot or in your garden (since celery is a cool weather crop, you'll need the temperature to be warm enough for growing but not too hot).