I have long held that buying a whole chicken is much more thrifty and economical than just buying parts. However, for some recipes you do need to know how to break down the bird into parts. It used to be that this was a skill everyone had (mainly because chicken only came whole) but it seems to have faded. Fear not! Here are some instructions, based on the ones in The Joy of Cooking.
1) With the bird breast-side up, cut the leg away from the body. Pull on the leg as you cut and find the hip joint. Cut all the way around the thigh on the back side of the chicken. Once the joint is exposed, crack it and the leg should come right off. Do this with the other leg, too. Set them aside.
2) pull the wings away from the body and cut around the joint. I usually leave a little bit of the breast attached to the wing to make a bigger serving. Once you find the joint, cut through it. I also remove the wing tips and reserve them for stock or give them to a deserving dog.
3) to separate the breast from the back, cut through the ribs on either side with a sharp knife or shears. Make sure to cut close to the backbone or you will lose some good meat. Reserve the back for stock.
4) To split the breast, find the wishbone–it is at the thick end– and scrape it free. Lay the breast skin side down. With a large, sharp knife cut through the breastbone down the middle. Sometimes you may want to quarter the breast. To do this, lay the breast skin side up and cut diagonally through it.
5) Now back to the legs: flex and crack the joint between the drumstick and the thigh. There is a thin layer of fat between these two pieces. If you cut along it they should separate with relative ease.
And now you should have a bunch of chicken parts and some stuff for amazing stock. Get cooking!