The basic fundamental stitch in knitting is called, appropriately enough, the knit stitch. In a knitting pattern it is represented by the abbreviation "k".

It's easiest to see what's happening in the English style.

Insert the tip of the right needle into the next stitch, from bottom to top (or left to right). The right needle should cross behind the left needle. The yarn is held behind the work.

With your right hand, loop the yarn counter-clockwise around the back (right) needle. This loop will become the new knit stitch.

Drag the tip of the right needle back through the stitch on the left needle, pulling the looped yarn through.

Allow the worked stitch to fall off the tip of the left needle. A new loop sits on your right needle; this is a new knit stitch!

I personally use the Continental style.

Insert the tip of the right needle into the next stitch, from bottom to top (or left to right). The right needle should cross behind the left needle. The yarn is held behind the work.

Bring the tip of the right needle behind the yarn held in your left hand.

Sweep the right needle down and back through the stitch on the left needle, bringing the working yarn with it.

Allow the worked stitch to fall off the tip of the left needle. The new loop sits on your right needle; this is a new knit stitch!