This is a short lesson in Western Swing or Texas contest-style backup guitar will present the basic concepts with some chord
arrangements of tunes.

This style of playing has a few defining characteristics:

a) Frequently changing chords, generally two per measure (in 4/4).
b) A walking bass line beneath the chords.
c) Frequent use of closed-position chords (i.e. with no open strings) instead of open-voiced chords (such as the standard G, C, etc.).
d) "Passing chords" used between the major harmonic areas in a tune.
e) Extended chords (6ths, major 7ths, 9ths, 13ths, minor 7ths, minor 9ths), altered chords (b9ths, augmented, diminished).
We want to use these techniques to transform the simple chord progressions that are found in many fiddle tunes and country
 tunes into more complex progressions _that will still fit the melody_. This is an important point: what you do still has to fit and
make musical sense. You probably won't want to use very complex chords like,  say, an A13b9sus4 in one of these progressions: 

A13b9sus4   +-+-+-+-+-+       

o | | | | o      5 +-+-+-+-+-+       

| | | | | |        +-+-+-+-+-+       

| | | o o |        +-+-+-+-+-+       

| | o | | |        +-+-+-+-+-+    

It probably won't work very well. But just use your judgment. If a chord sounds good then it's good.

These are essentially jazz-based techniques, and it helps to have at least some knowledge
of jazz harmony to get a grip on this stuff.
The discussion does get a little technical,
but even if you don't understand the theory, just try playing through the examples -
they're a lot of fun and they sound really cool.

Listen to recordings by the great Bob Wills and the Texas Playboys for good examples of this type of backup playing.
The Texas Playboys guitarist, Eldon Shamblin, is responsible for much of the development of this style as it is applied to
country-style tunes. Another great group to listen to if you want to hear this stuff in a more traditional jazz setting is the
Quintet of the Hot Club of France, with the virtuoso Django Reinhardt on guitar. Another master practitioner of this style
is Ranger Doug from Riders in the Sky.

Here are some chord changes to help you get started

  A       A9/C#     D       D#o7      A       A#o7      Bm7     E7 
------------------|-----2-------2----|------------------|-----2-------0---||
-----2-------5---|-----3-------1---|-----2-------2---|-----3-------0---||
-----2-------4---|-----2-------2---|-----2-------0---|-----2-------1---||
-----2-------5---|-0-------1-------|-----2-------2---|----(0)------0---||
-0-------4-------|-------------------|-0-------1------|-2-----------2---||
------------------|-------------------|------------------|---------0--------|| 

A       A9/C#     D       D#o7      E7      F#m       E7/G#   A
-------------------|-----2-------2--|-----3-------5---|-----7-------5----||
-----2-------5---|-----3-------1---|-----3-------5---|-----5-------5----||
-----2-------4---|-----2-------2---|-----4-------6---|-----7-------6----||
-----2-------5---|-0-------1-------|-2-------4-------|-6-------7--------||
-0-------4-------|------------------|------------------|--------------------||
-------------------------------------|-------------------|-------------------|| 

A       A7/G      D/F#    Dm/F      A/E     D#o7      E7/D    E7/B

-----5-------5---|------------------|-------------------|-------------0----||
-----5-------5---|-----7-------6---|-----5-------7---|-----5-------0----||
-----6-------6---|-----7-------7---|-----6-------5---|-----4-------1----||
-7-------5-------|-----7-------7---|-----7-------7---|-----6-------0----||
------------------|-9-------8-------|-7-------6-------|-5-------2--------||
------------------|------------------|-------------------|-------------------|| 

A       A9/C#     D       D#o7      E7      E7/B      E7/G#   A

------------------|-----2-------2---|------------------|-------------------||
-----2-------5---|-----3-------1---|-----5-------5---|-----3-------2----||
-----2-------4---|-----2-------2---|-----7-------7---|-----4-------2----||
-----2-------5---|-0-------1-------|-----6-------6---|-----2-------2----||
-0-------4-------|------------------|-7----------------|---------0--------||
|-----------------|------------------|---------7--------|--4----------------||

An important point about this backup style is the articulation. You should strive for a sound like this:

boom-CHUNK-boom-CHUNK-boom-CHUNK-