How to Hold Hook and Yarn

First you have to know that there are several ways to hold the hook and yarn.  I'm going to show you both here and then most of the rest of my pictures will show my hands demonstrating in the way that I crochet.  Whichever way you choose, just know that it is really hard to switch to another way, so you'd better like the one you pick.  I do switch a little to relieve tension in my muscles, but it is really awkward.

This way, you are holding the hook like you would hold a pencil.

This way is more like just holding your hook in a loose fist while you pinch the spot made for your thumb.

Next, the yarn.  After you've made a slip knot, you hold the yarn in your three lowest fingers.  Some people also wrap the yarn around their pinky finger.

Then, you wrap your fingers around the yarn.

Now, here comes another difference.  Although the yarn stays in the same place, you will either pinch the tail with your middle finger and thumb as in this picture....

Or pinch it with your forefinger and thumb, as shown here.

(This picture is the way I hold the yarn, and is 'technically' the wrong way.  It works great for me.)