You can find an updated version of this article in the Encyclopedia of Tunisian Crochet!
Tunisian Crochet 101  (See Diagram at bottom of page)

Tunisian Crochet has a two step method in forming stitches. The first step is known as the Forward where the loops are gathered on the hook working from right to left.  
The second step is known as the Return where the loops are connected to one another and dropped off the hook. The Return is worked from left to right.

In Tunisian Crochet, the Front of the piece always faces you.  Since the stitches are formed with a Forward and Return steps you never need to ‘turn’ the piece around.

Tunisian Crochet has tight dense stitches that are well designed for winter blankets and outer wear garments that will keep the cold out.  To soften the stiff nature of Tunisian Crochet you must use a hook that is one to three sizes larger than you normally would for the size of yarn/thread you are using.

Tunisian crochet tends to get looser at the finished end as opposed to the starting end.  To counteract this, use a hook one size larger to make the beginning chain, or work your chains very loosely when using larger hooks.  Sometimes using a larger hook for the chain can result in the bottom edge being larger than the top edge. Some experimenting will help you find the best method to keeping the finished piece the same width at both ends.

When working the beginning chains for Tunisian Crochet, ALWAYS ADD 2 CHAINS to the desired number of chains.  This will allow you to create the edge of your piece- using the basic stitch formation-on the first and last stitches of the row, so you don’t break the pattern of your piece.

To create a more solid edge, I don’t follow the generally accepted method of forming the last stitch on a row.  I gather the loops on the hook as I normally do for the Forward step, except for the last stitch.  There are three threads that form the last stitch.
They will look similar to this: ()|

Insert the hook between the threads, so that you have 2 (two) threads on the outside edge of the piece. ()*| With this diagram, place the hook where the * is.
Yarn over, and pull the loop up on the hook and finish as you normally would for the Return step. This creates a much more solid stitch on the outer edge of the piece.

Tunisian Crochet is well adapted for changing color of yarn.  With practice and patience, you can use Cross Stitch patterns to create designs in the crochet.  

Many people will work the main piece in one color and then Cross Stitch the pattern on top, however; the pattern can actually be crocheted into the piece, much like those fancy machine knitted sweaters you see in the department stores.

Tunisian Crochet Foundations: The Basic Five
The Simple Stitch Foundation is formed by slipping the hook under the vertical thread on the front of the piece.  This is what Americans call the Afghan stitch.

The Knit Stitch Foundation is formed by inserting the hook through the center of the stitch to the back of the piece before pulling a loop onto the hook.  The appearance of this stitch mimics the common Stocking stitch in knitting.

The Full Stitch Foundation- also called the Plain st- is formed by inserting the hook between the stitches to the back of the piece before pulling a loop onto the hook. This gives the front of the piece a very smooth appearance, but this foundation curls quite badly.

The Purl Stitch Foundation is something I have seen only one other printed publication use besides me.  I form the stitch by slipping the hook under the vertical thread, on the back of the piece, before pulling a loop onto the hook.  This mimics the Purl stitch in knitting.

The Reverse Stitch Foundation is what most folks associate as the Purl stitch of Tunisian Crochet.  Both the Reverse and what I call the Purl stitch create the same visual patterns, but the front and back of each foundation is reversed from the other.

The Reverse Stitch is formed by pulling the yarn to the front of the piece, then slip the hook under the vertical thread of the next stitch, as you normally would for the Simple Stitch.  Now, pull the yarn down under the hook, before wrapping it over the hook.  Pull through and leave the loop on the hook.
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Tunisian Crochet
is one of the most misunderstood (or perhaps forgotten is a better word) forms of crochet in the U.S.
Most of us learned the Afghan stitch at sometime, but no one ever showed us the wonderful diversity of Tunisian Crochet.  We Americans simply didn’t have much information on it.  From books printed in Europe and other countries, plus some reproductions of historical crochet books, I have discovered a myriad of stitches available in Tunisian Crochet.
 Front Vertical            Cross/Horizontal
    Thread                                   Bar
Back Vertical            Cross Bar  
     Thread                   Space