For a handgun, you have to have a permit to purchase. If you have that, you can bring the gun home the same day. If you don't have a permit to purchase, you'll need to go to the county sheriff's office to apply for one. You have to go to the county sheriff's office in which your driver's license says you live. It becomes active three days after the date of application.
For other guns, I don't think there is a waiting period at all. They call it in from the store, I believe.
What are you getting?