Check your chicken prices, and you'll find that buying a whole chicken is amazingly cheaper than purchasing parts someone else has prepared for you. Yes, you are buying bones - but with a nice-sized bird, you'll have about six cups of meat for your efforts (if you're making a cassarole or soup or salad, etc.)
There are different ways to cut the chicken. If you are frying or baking, then you'll want wings and thighs - the standard assortment of pieces. For that, the technical term is "quartering the chicken."
If you want boneless, skinless chicken breasts, that's called "boning the chicken." You're seperating all the breast meat from the remainder of the bird, and you can "butterfly" that breast as well. That's separating it into two, thinner sections.
Food Network has online videos and print-out instructions for each of these techniques. Cooking for Engineers has a great list of instructions for cutting up a whole chicken, accompanied by clear photos. Hormel Foods also has nice sets of instructions, with step by step photos that are excellent. Hormel has lots of info: cleaning, brining, lots of stuff here if you're really into this subject....