President Grover Cleveland dedicated the Statue of Liberty on this date (October 28th) in 1886. Construction in Paris took almost ten years and when completed, the statue was disassembled into 350 pieces, shipped across the Atlantic and reassembled on her pedestal.
 
Everyone knows that Lady Liberty was a gift from France, but more appropriately we should say a gift from the French. As B.K. Marcsu explains in Lady Liberty: An Unauthorized Biography [Hat-tip: UncleGlenn] ~

France’s national government did not contribute, but thousands of French schoolchildren made small donations. A copper company donated the metal sheets that would form the statue’s skin.

There was also a lottery held by the French-American Union, with prizes donated by Paris merchants. At one point the sculptor, Frédéric Auguste Bartholdi, even charged admission and sold souvenirs.
 
In America the government didn’t have much to do with funding either, other than providing the small island for the statue to stand on. It was newspaper publisher Joseph Pulitzer who got behind the project and;

… began a popular campaign for private donations to complete the base of the statue. His campaign attracted more than 120,000 contributors. Most gave less than a dollar.

Interestingly, Bartholdi originally had a completely different concept and location in mind for his project.

The original statue was to be an Egyptian woman—a fellah, or native peasant—draped in a burqa, 😯 one outstretched arm holding a torch to guide the ships on the great waterway over which she would stand.
 
Bartholdi had wanted to place his piece at the northern entrance to the (recently completed) Suez Canal in Port Said because the canal represented French greatness in general and engineering greatness more specifically. His statue was to be a synthesis of French art and French engineering, as well as a political symbol of the progress that France offered the East.

 
Apparently he couldn’t generate enough enthusiasm for an “Egypt Enlightening the World,” so he had to go with plan B.
Happily, Egypt’s loss was our gain.

 
Lady Liberty has been holding freedom’s torch over New York Harbor for 127 years now.