The term "composition" refers to composed, artistical chess problems and endgame studies, not positions that have appeared in real play, and presented as problems to be solved ("This position occurred in a recent game. How did White win?").
All the books mentioned here assume that the reader is familiar with the rules of chess, and understands the movement and powers of the pieces.
The best introduction that is still generally available is probably Kenneth S. Howard: How to Solve Chess Problems, Dover Publications.
John Nunn: Solving in Style, London: Allen & Unwin, 1985, is also a very good place to start, especially for 'ordinary' chess players. Happily, this title is now back in print (London: Gambit Publications, 2002).
John Rice's Chess Wizardry: The New ABC of Chess Problems, London & Seattle, 1996, covers a much larger area than two works mentioned above. It is not for the absolute beginner, but could be profitably read by someone who has studied either of the works mentioned above.
The best introduction is John Roycroft: Test Tube Chess, 1972, (revised edition published by Dover Publications in 1982 under the new title The Chess Endgame Study). It is unfortunately out of print, but if you can pick up a copy second-hand, do so. Covers a surprisingly wide area: not only is the technical side of the endgame study described, but also subjects such as tourneys, composition, cook-hunting, and much more.
John Beasley & Timothy Whitworth: Endgame Magic, London & New York, 1996. Still in print, or available from major chess shops. Good introduction with detailed description of the solutions of the studies presented.
(John Nunn's Solving in Style, mentioned above, also covers endgame studies.)
A good starting point for finding out-of-print books through the Internet is www.bookfinder.com .