Collect the discarded vegetable tops of carrots, parsnips, beetroot and turnips - they don't need to have any green growth but do need to have the part where the leaves came from, at the top.
Chives and leeks are other examples of plants you can easily grow from the 'base' in the same way as celery.
Discarded vegetable scraps
Saucers or jam jars
If you are successful in growing some green leaves you could then put the plants into a pot of soil. Depending on the time of year, grow them outside and you may be lucky and see your plant flower!
In a saucer on a sunny windowsill you can expect to see some green, leafy growth. Tap roots such as carrots, beetroot and parsnips will not re-grow.