The object of Lines of Action is to get all your pieces into a single connected group. A group of pieces is connected if they occupy an unbroken chain of adjacent spaces, horizontally, vertically, or diagonally. The rules for Lines of Action were published in Sid Sackson's book, Gamut of Games, A.
Full rules and examples of play can now be found from the following website:
http://www.boardspace.net/loa
The commercial edition of this game is available as part of the Abacus wood box series, but all you really need is a checkerboard and checkers.