Like a knife
Pick up the needles, one in each hand, as if you were holding a knife and fork—that is to say, with your hands lightly over the top of each needle. As you knit, you will tuck the blunt end of the right-hand needle under your arm, let go with your hand and use your hand to manipulate the yarn, returning your hand to the needle to move the stitches along.
Like a pen
Now try changing the right hand so you are holding the needle as you would hold a pen, with your thumb and forefinger lightly gripping the needle close to its pointed tip and the shaft resting in the crook of your thumb. As you knit, you will not need to let go of the needle but simply slide your right hand forward to manipulate the yarn.
As you knit, you will be working stitches off the left needle and onto the right needle, and the yarn you are working with needs to be tensioned and manipulated to produce an even fabric. To hold and tension the yarn you can use either your right or left hand. Try both methods to discover which works best for you.
Yarn in right hand
With the ball of yarn on the right, catch the yarn around your little finger then lace it over the third finger, under the middle finger, and over the first finger of your right hand.
Yarn in left hand
With the ball of yarn on your left, catch the yarn around your little finger then take it over the third and middle fingers. Most left-handed knitters will also find that, even if they reverse the direction of knitting (working stitches off the right needle onto the left needle), using the left hand to manipulate the yarn will be easier to manage.