Everyone has their own personal way of holding the hook and controlling the yarn in crochet. Righthanders hold the hook in their right hand, usually a: as though it were a pencil; or b: in a firmer, overhand grip.
c: The left hand holds the work and at the same time controls the yarn supply. If you prefer, the left hand index finger can be used to manipulate the yarn, while the middle finger holds onto the work.
d: To maintain the slight tension in the yarn necessary for easy, even working, it can help to arrange the yarn around the fingers of the left hand in this way.
The Base Chain
Almost all crochet starts with a base (or foundation) chain. This is the equivalent of ‘casting on’ in knitting. The base chain is a series of chain stitches, which normally begin with a loop secured by a slip knot.
Slip Knot
a: Make a loop; hook another loop through it. b: Tighten gently and slide the knot up to the hook.
Chain Stitch (ch)
a: Wrap the yarn over the hook in an anticlockwise direction (or hold the yarn still and manoeuvre the hook); b: draw the yarn through to form a new loop without tightening up the previous one.
Note: Unless otherwise specified, always wrap the yarn this way round.
To make a length of base chain, make as many chains as required. Hint: Keep shifting your left hand position up close to the hook every couple of stitches or so; this is easy, if you use a right hand finger tip to hold down the loop on the hook, while you do so.
To count chains correctly as you make them, do not count the initial slip loop as a chain. To count them afterwards, first make sure that they are not twisted and that you are looking at the ‘front’ c: then count back, but ignore the loop still on the hook. 
Double Base Chain
Hint: You may find that a base chain of double chain is not only more flexible than one made of single chain, but also easier to make, to count afterwards and to work back into.
a: Make 2 single chains; b: insert the hook into the 2nd chain from the hook (i.e. the first chain made) and work one single crochet (see Single crochet) c: insert the hook into the single vertical thread which forms the lefthand side of’ the previous single crochet and work another single crochet; repeat this last step.
Slip Stitch (sl st)
a: Insert the hook into the work (into the 2nd chain from the hook), wrap the yarn over the hook, draw the yarn through the work and the loop on the hook in one movement -that is one slip stitch completed; repeat this last step, b:. 
Single Crochet (sc)
a: Insert the hook into the work (into the 2nd chain from the hook), wrap the yarn over the hook and draw the yarn through the work only, b: wrap the yarn again and draw the yarn through both loops on the hook c: 1 single crochet made. 
Half Double Crochet (hdc)
a: Wrap the yarn over the hook and insert the hook into the work (into the 3rd chain from the hook), b: wrap the yarn over the hook, draw through the work only and wrap the yarn again; c: draw through all 3 loops on the hook. 
Double crochet (dc)
a: Wrap the yarn over the hook and insert the hook into the work (into the 4th chain from the hook); b: wrap the yarn over the hook, draw through the work only and wrap the yarn again; c: draw through the first 2 loops only and wrap the yarn again; d: draw through the last 2 loops on the hook. 
Treble (tr)
a: Wrap the yarn over the hook twice and insert the hook into the work (into the 5th chain from the hook); b: wrap the yarn over the hook, draw through the work only and wrap the yarn again; c: draw through the first 2 loops only and wrap the yarn again; d: draw through the next 2 loops only and wrap the yarn again; e: draw through the last 2 loops on the hook. 