Cut the base off of the stalk just like the photo below, and place it in a small bowl or saucer with warm water. It gets the celery a kick start for regrowth. Leave it there for about a week. During that week the outer stalks will dry up. The inside leaves will become a nice green, and start getting fuller and growing taller. Change the water every couple of days while in this phase, and using a spray bottle- spray water directly down into the new growth. After the week has past. It is time to plant it! You can do this indoor or outdoor based on where you live/season.
Outdoor- dig a small hole, and fill it with water. With stalk side up- Put it in the water filled hole. Cover it up and leave an inch of soil on top. Water thoroughly.
Indoor- Place a thin layer of mulch in the bottom of the planter for drainage. In the planter use a mix of dirt and potting soil. Place the base far enough down to cover the stalks completely, and water thoroughly.
Celery grows very well with an abundance of water. Once the celery is fully grown cut the roots off. Cut the base. Soak it in warm water, and do it all over again! Save yourself some money and get soaking!
These last photos are located from 17 Apart. She did a full tutorial which is one of my sources-indoor potting(see here), and Providence Acres is the other for outdoor planting(see here).