you get a collectors authentication slip from the fair with the collector's signature on it it's as good as a permit for owning it until you get onto your own property but its dated and each one looks different to avoid forgery. Also, if the weapon is caught off of your property, or in some cases, even just outside of your house can be a felony due to it being strictly a "collector's piece for display purposes only"
but this only goes for things like RPGs and things you arent normally suppose to own at all. As for handguns/shotguns/etc you have a certain amount of days to get the weapon licensed under your name or it can be a felony. I'm not 100% sure on the laws, but keeping a handgun from a collector in your home without getting it licensed is fine, but if its a weapon you are going to have with you, or a weapon you are going to take hunting if youre caught out and about with the weapon I believe its a felony.
Also I live in Missouri. And these might not be 100% accurate as I live with my mother currently, and she doesn't like firearms of any kind, the last time I was at a gun fair was when I was 18, and laws do indeed change ALOT within 2 years. However, through talking to people that share a similar interest in guns, I do know for a fact that youre still able to go to a gun fair and pick up any kind of weapon and take it home that day.
I'm not sure if you still have to go straight home with the weapon, as I know if you have the gun and tell a cop that you just got it or something along the lines of not had the given time to get it registered yet and its not hidden on your body (if its hidden and you dont have a concealed weapons license no matter what its a felony), they will give you a warning and its put into the system, but if you are caught again, it will show up you have had a warning and how long ago the warning was given, if the 2nd cop believes you have had time to get the weapon registered you could be arrested for it.
Also, if you are interested in buying a gun in the USA, if you buy it from another person and not a collector or a store, get it registered as soon as possible ESPECIALLY if you got it for really cheap. I could have gotten a gun about a year ago, hand gun for 50$ USD. the catch? It was the murder weapon in a double homicide in Illinois. Every weapon leaves a very unique signature on a bullet it fires, 5 handguns made by the same company on the same day using the same mold will all leave different scratches and such on the bullet after the bullet is fired. So carrying the gun unregistered that has been used in a murder, and getting caught with the weapon will automatically get you questioned for murder, and unless you can provide the person who sold it to you's name, and when you bought it, etc you will most likely also be arrested and charged with murder and your only hope is to convince the jury that it was bought AFTER the murder during court.
When getting the weapon registered if it has been used in a crime, it will be registered in your name and all the stuff will take around a week, but a cop will show up at your door and take you in for questions, usually you will not be a suspect, but will be asked where and who you go the gun from, and not having that information may cause suspicion and cause you to be a suspect.
When I turn 21 I plan on getting a bounty hunting license and a concealed weapons license. The concealed weapons license costs around 200 - 300 $ USD and all that is required it paying the money and taking a 7 hour class, in which you be given a test and must pass the test to get the license.
The bounty hunting license I'm not as sure about. I know you also have to take a "class" and a test, but I have no clue on the cost of the class/test or how many hours or how many "classes" you have to go to before being able to get the license.