#1 Always start with a sharp knife
Though it may sound contradictory, a sharp knife actually lessens the chance of injury. Duller blades force a person to push harder as they slice, increasing the chance for the blade to slip and cut into fingers. To keep blades in tip-top shape, wash by hand immediately after use. Do not leave knives in the sink or place them in the dishwasher. Store them either on a magnetized strip or in a wooden block. Knives stored in a drawer get jostled together, dulling the blades. To learn how to sharpen your kitchen knives, check out this video: http://www.youtube.com/watch?v=12vp7eheIcY
#2 Make sure you have a clean, flat, and stable work surface
Nothing is more dangerous than chopping on a wobbly work surface, or trying to cut in an overly-cramped space. Make sure the table or countertop surface you will be working on is stable and has enough room to at least accommodate a full size chopping board.
#3 Master the proper knife grip
The way you grip your knife is crucial to knife safety. The more secure the knife is in your hand, the more precise your cutting skills will be. Always hold the butt of the knife in the palm of your hand, gripping with your pinky, ring, and middle finger, and pinching the top of the blade between your forefinger and thumb. This gives you a nice, tight hold on the knife.
The opposite hand, (or guiding hand) which will be holding the vegetable, should also be held a certain way to avoid slicing your fingers. Grip the item you are cutting in the palm of your hand, steadying the food with three fingers- the ring and forefinger together with the middle finger in front- it should look like you are making a claw. See a picture of what this looks like here. The tips of the fingers should be either straight down or curled very slightly back, while the knuckles will serve as a guard for the blade, keeping it away from your precious digits. This is the proper form for holding and cutting with a knife. From here you will be ready to learn the basic knife cuts:
#4 The Dice
The dice is one of the most basic of knife skills, and pretty easy to master. The idea is to create uniform cube shapes to create a nice visual appeal, as well as an even cooking time. To begin with, you will have to square the item you are chopping, by first removing the top and bottom, and then slicing down the length creating four even sides. This will ensure that the dice will be uniform.
For a 1/2″ dice, slice the item lengthwise 1/2″ in from the edge. Repeat, cutting 1/2″ in from the cut you just made. When you have finished cutting the length, turn the item 90 degrees and begin cuts 1/2″ from the edge, this time going width-wise. You should end up with perfect 1/2″ cubes.
To dice an onion, peel the onion and slice in half lengthwise. Be sure to leave the root on, since this is what will hold the onion together as you chop it.
Make several slices going from the top of the onion to the root, being careful not to slice through the root.
Now make a horizontal slice about halfway up the onion, again, going from the top of the onion to the root. This will ensure a more uniform size in the dice of the onion.
Now, go ahead and chop the onion, working from the top to the root. You should end up with a nice, even dice.
This is a popular cut used in stir fry recipes and other Asian cuisine. The secret to a really good julienne is a very sharp knife. If you are going to julienne a round vegetable, like carrots, slice the vegetable lengthwise to create a flat edge for it to rest on. This way, it wont roll around while you try to slice it. Start by making thin slices lengthwise (they should look like very thin planks). Then stack these planks and slice lengthwise again. Voila! You should now have a julienned vegetable. (Click here to watch a chef julienne a carrot in this YouTube video)
#6 Allummette (al-yoo-MET)
Also known as a matchstick cut, measures 1/4″ by 1/4″ by 2 1/2″ long. To give you an idea, this would be about the size and shape of your basic fast-food french fry. Alternately, the thicker version (think steak fries) are called Batonnet and measure ½ inch × ½ inch × 2½-3. Create Allummette or Batonnet the same way you would the first few steps of a dice.
#7 Brunoise (BROON-wahz)
Is basically a very small (1/8″ by 1/8″ by 1/8″) dice. To make a brunoise cut, julienne the vegetable, then then turn a quarter turn and dice again, making 1/8″ cuts down the length to create a uniform cube shape.
Is a cut used on herbs that creates thin ribbons, much like confetti. To chiffonade, stack the leaves and roll them tightly into a cigar shape. Slice across the width of the roll, working your way down. When you are finished slicing, separate and fluff the shreds with your finger tips.
For more information on these cutting techniques, and to see what each one looks like, check out this helpful page: http://culinaryarts.about.com/od/knifeskills/ig/Basic-Knife-Cuts—Shapes/