What is required to buy a hunting rifle in Oregon?

You need to be over the age of 18. You must not be a felon or under a restraining order. Go to a gunshop with your ID, find the gun you want, fill out ATF form 4473. The gun store will call the FBI and do a background check, called a NICS check(National, Instant, Check, System). If you come back clean, pay your money, grab your firearm and leave. Some people(Military, people with security clearances, people with names similar to known felons) may be delayed, in those cases you come back in 3 days and usually may pick up your firearm then.

Really very easy.