Just like the first step to fighting crime is learning how to put on a cape, the first step to perfect knife skills is learning how to hold a knife.
There are two basic grips: the handle grip, and the blade grip. If you've only ever been using the handle grip, give the other one a try—you may find your cuts improving dramatically. There's not much more to say that the following images don't explain, so I'll depart from usual form and cut myself short.
That's good news if you're into the whole brevity thing.
The Handle Grip, Front View
With the handle grip, your hand is completely behind the bolster on the handle itself. It is generally used by beginning cooks, or cooks with exceptionally small hands. It's comfortable, but offers only limited control when doing precision knife work.
The Handle Grip, Back View
Same grip, from the back. All the fingers are tucked behind the bolster.
The Blade Grip, Front View
The blade grip is the preferred grip for more experienced cooks. Your thumb and forefinger should rest in front of the bolster (the area where the metal flares out to meet the handle) directly on the blade. It's a little intimidating, but it offers much better control and balance. This grip may be difficult and/or uncomfortable on cheaper stamped knives that don't have a bolster.
The Blade Grip, Back View
Same grip, from the back. Notice the first finger is in front of the bolster.
When cutting foods, always place them in a stable position, preferably with a cut surface flat against the cutting board. Guide the knife blade against the food with your free hand. Protect your fingertips by curling them inwards, using your knuckles to guide your knife.
A fine mince requires the use of your free hand. Place the tip of your knife on the cutting board and hold it in place with your free hand. Rock the blade up and down to reduce herbs (or anything else) to a fine mince.