
In response to the killing, George Grinnell founded the first Audubon Society in 1886 to organize opposition. Among Grinnell's proposals were laws to protect wild birds. His organization quickly collapsed, however, largely due to financial difficulties, and it failed to have any effect on the slaughter.
In 1896, Harriet Lawrence Hemenway took up the cause of stopping the trade in bird parts. She persuaded influential friends to pledge to stop wearing bird feathers and to promote the cause among other high society women in Boston. She and her associates founded the Massachusetts Audubon Society to advocate on behalf of wild birds. Bird watching was just then becoming a popular pastime, so she found many willing to help her cause.

Eventually activism on the part of bird watchers and ornithologists led to legislation. Several states passed laws based on Grinnell's model; however, enforcement remained spotty. The Lacey Act, in 1900, banned killing birds illegally in one state and then selling them in another. In 1913, Congress followed it with the Weeks-McLean Migratory Bird Law, which placed migratory birds under federal jurisdiction and prohibited their killing without authorization from the federal government.
Several state and federal courts struck down the 1913 law as a 10th Amendment violation. (Such a law would probably pass review today, due to changes in constitutional interpretation in the wake of the New Deal.) The Wilson administration found a way around the rulings by negotiating a treaty with the British Empire (on behalf of Canada). The 1916 treaty contained all of the protections sought under the Weeks-McLean Law and had the additional benefit of protecting birds on both sides of the U.S.-Canadian border. Congress enacted the treaty as the Migratory Bird Treaty Act in July 1918. Later revisions to the law extended its protections to include similar treaties with Mexico, Japan, and the Soviet Union (now Russia).

A list of protected birds is available here. Introduced bird species (like house sparrows and mute swans) and captive-bred game birds (like domestic mallards) are not protected by federal law.
The background history of the MBTA is included in chapter 5 of Scott Weidensaul's Of a Feather, which I reviewed in December.