With proper system design, an antenna tuner or transmatch can allow a non-resonant antenna to operate nearly as efficiently as one that is carefully cut to resonance.  These articles and links will help you understand what needs to be done to  make and use effective an antenna system using a transmatch.

• Do You Need an Antenna Tuner?
  QST January 1994, pp. 70-72
  Maybe yes, maybe no. It all depends on the type of antenna and feed line you're using.
  
• A Balanced Balanced Antenna Tuner
  QST February 1990, pp. 28-32
  Build the right antenna tuner to use with your balanced, open-wire-feed antenna.

• A Better Antenna-Tuner Balun by Andrew Roos ZS1AN
  QEX September 2005 pp 29-34.

• An Automatic Antenna Tuner: the AT-11
  QST January 1996, pp. 35-39
  This easy-to-build, fully automatic tuner.

• Getting the Most Out of Your T-Network Antenna Tuner
  QST January 1995, pp. 44-47
  Here's how to adjust this popular tuning circuit so it transfers maximum power to your antenna.
• How to Evaluate Your Antenna Tuner - Part 1
  QST April 1995, pp. 30-34
  With some simple low-power measurements you can learn a lot about your antenna tuner. There may be some real surprises.
• How to Evaluate Your Antenna Tuner - Part 2
  QST May 1995, pp. 33-37
  AI1H shows data taken using a low-power SWR tester and his simple load boxes to evaluate several antenna tuners.
  For information on a different but related subject, see Transmission Lines/SWR
• The EZ-Tuner Part 1
  QST April 2002, pp. 40-43
  This could be one of the most versatile homebrew antenna tuners ever created.
• The EZ-Tuner Part 2
  QST May 2002, pp. 28-34
• The EZ-Tuner Part 3
  QST June 2002, pp. 33-36

• Simplified Design of Impedance-Matching Networks, Part I of III by George Grammer W1DF.  March 1957 QST p.38-42.

• Simplified Design of Impedance-Matching Networks, Part II of III by George Grammer W1DF.  April 1957 QST p. 32-35.

• Simplified Design of Impedance-Matching Networks, Part III of III by George Grammer WDF.  May 1957 QST p. 38-42.

Kevin W9CF has a nifty transmatch simulator—not only does it have an auto-tune function, but it calculates the loss in the tuner!