It just depends on your prescription and whether the contacts you want to get are in stock or not. Most places have a large inventory of contacts, and you can possibly get them back the same day. If your lenses are not in stock, you may wait for a day or two to get them.
Usually there are a large amount of contacts in stock and you can get your contacts the same day as you have your eye exam. If the contacts you want to get are out of stock, it will take you 2 or 3 days to get them back.