As others have noted, attempts at gun control goes back a long time. However, I think we can mark the 1968 Gun Control Act as the start of the serious, "modern" attempts at gun control. It went through following political assassinations of John F. Kennedy, Robert F. Kennedy, and Martin Luther King, Jr.
Before the act you could simply order a gun through the Sears Roebuck catalog and many others and have the gun mailed directly to your residence. Lee Harvey Oswald killed JFK with a rifle he ordered through the mail, using an alias. Attempts to limit interstate sales began. The 1968 bill was stalled in Congress but went through following the assassinations of RFK and MLK. It prohibited interstate transfers of firearms except through FFLs.
Attempts to further regulate guns have been subsequently made at the federal level, some successful and some not.