"SF looks towards an imaginary future, while fantasy, by and large, looks towards an imaginary past."
- Frederik Pohl

This describes the preparation of the sail material:

Around the hull swung the gleaming hoop, and now the carrier brought up the sail, a great roll of darkly shining stuff. When unfolded and unrolled, and unfolded many times more, it became a tough, gleaming film, flimsy as gold leaf. Unfolded to its fullest extent it was a shimmering disk, already rippling and bulging to the light of the sun. The cadets fitted the film to the hoop, stretched it taut as a drumhead, cemented it in place...

Johannes Kepler speculated that comets' tails are bent by the sun's action in his 1619 book Opera Omnia. Newton thought it was possible that light would exert pressure on material bodies. The existence of light pressure was demonstrated in theory by James Clerk Maxwell in 1873. Laboratory experiments confirming the theory were performed in 1910 by P.N. Lebedev, a Russian physicist, who overcame great difficulties in measuring the 4.7 x 10-6 N/m2 pressure of noon sunlight here on Earth. In the 1920's, Konstantin Tsiolkovsky and Fridrich Tsander wrote about "using tremendous mirrors of very thin sheets... using the pressure of sunlight to attain cosmic velocities."

The first mention of solar sails in a science fiction publication was not in a story; it occurred in the May 1951 issue of Astounding Science Fiction. Carl Wiley published an article called "Clipper Ships of Space."

The first publication directly describing space sailing was probably The World, The Flesh and the Devil (1929) by JD Bernal.

The very first science fiction story about solar sails was probably "The Lady Who Sailed The Soul" (1960) by Cordwainer Smith. The story takes place thousands of years in the future - "Out of it all, two things stood forth - their love and the image of the great sails, tissue-metal wings with which the bodies of people finally fluttered out among the stars." (See the entry for starlight sail.)

The first person to suggest solar sailing was probably Johannes Kepler, in a 1608 letter to Galileo: "Provide ships or sails adapted to the heavenly breezes, and there will be some who will brave even that void.”

In 1958, NASA launched Echo 1, the first U.S. passive communications satellite. It was an aluminum-coated Mylar plastic balloon (microwaves bounced off it). Echo 1 is the first time NASA included solar pressure in calculating trajectory. Once in orbit, solar pressure moved the "sateloon" but didn't collapse it.

Apparently, some projects have already been tried to attempt to prove the real-world feasibility of light sails. Reflective panels may be used to slowly steer spacecraft, conserving fuel better used for maneuvering. A similar sort of scheme involves using lasers to push on a solar sail, thus powering a ship from a distance; see laser cannon, from Mote in God's Eye by Larry Niven and Jerry Pournelle.

As far as I know, the first use of the phrase is from Think Blue, Count Two (1962) by Cordwainer Smith; see light-sail ship.