There are two main ways to hold your yarn while knitting, but with practice, both styles can be done quickly and produce the same results.
Holding your working yarn in the left hand is called Continental (or European) knitting, and requires less hand movement. Holding it in the right is called American (or English) knitting.
Which one should you choose? The difference is mostly personal preference. I usually teach Continental first, as it requires less hand movement and therefore less repetitive stress on the joints. If you find it tricky to keep your tension correct or master the motions required, try American. As you become more experienced, you will sometimes find reason to use both on the same project (as in when working two colours in stranded knitting).
In knitting lingo, American style is sometimes called "Throwing", because of how you have to "throw" the yarn around the needle to create a new stitch, and Continental is called "Picking", since all you need to do to grab the new yarn is pick it up with a small needle movement. The battle of throwing vs. picking rages on, but all in good fun, and truly--it is up to the comfort of you, the knitter, to determine which is best for you.
The first important thing to learn when you knit is how to keep good tension on your working yarn. Keeping good tension makes it easier to form stitches, and the resulting stitches are more even. Poor tension makes knitting difficult, frustrating, and the results shoddy-looking.
Good tension is created by always keeping your working yarn taut. If you are having trouble forming stitches, this is usually one of the main culprits.
How you keep your yarn taut will be determined by your style of knitting, or which hand you are holding your working yarn in.
Holding the Yarn for Continental Style
Continental knitting holds the yarn in the left hand.
You do not need to wrap your hand exactly the way I do, but it is important that however you wrap the yarn, it keeps a firm tension on the working yarn while allowing it to slide smoothly over the hand.
Holding the Yarn for American Style
This is much less particular than Continental, as the tension is made by pulling on the yarn after it has been looped around the needle. You'll see what I mean when we get to the nitty-gritty of knitting in this style.