That all depends on where you're from, as we host questions from all over the world, and laws pertaining to firearms ownership vary greatly between countries.
In the US, the answer is generally no, with the exception of Illinois, which requires a buyer to obtain a Firearms Ownership Identification Card. Otherwise, you only need special permits if you're buying a short-barreled shotgun (barrel length of less than 18 inches), or one which is classed as an NFA Destructive Device (fixed magazine capacity of more than ten rounds - specifically, the Amstel Stryker and Protecta - also referred to as the "street sweeper").
You need enough money to purchase the shotgun, a state or federal issued identification card, and, under certain circumstances, you'll need proof of address (specifically if buying it in a state other than the one you live in), or copies of military orders assigning you to be stationed in that state (if it's a different state than your Home of Record). And Illinois residents will need their FOID card. You'll fill out the ATF Form 4473, the dealer will phone into NICS to conduct your background check, and, if you get a "proceed", that's pretty much all their is to it.
To get a gun license you would need to go into a gun store in the town you live in and ask for the information you need.
yes
No
No.
no
No
no
No state requires that shotguns be licensed.
yes, you just need a license
Generally, no.
No.
No ... but their may be an age requirement.