Learning how to cut up a whole chicken is very useful. First of all, because whole chickens are much cheaper than chicken pieces.
Second of all, the butchers at the grocery stores aren't usually too careful when they're slaughtering the chickens into pieces. By cutting the chicken yourself, you will end up with very neat, even pieces.
It's very easy to do too. With just a little practice, you will feel like a cooking pro.
The most important thing when starting this task is a bit of courage, a big plastic cutting board, and most importantly, a SHARP knife. It's much easier to cut yourself with a dull knife than with a sharp knife, believe it or not.
Place the chicken breast side up, pointing toward yourself. Make an incision in the skin right between the thigh meat and the breast meat. 
With your hands, grip the thigh and the breast meat and bend the thigh back. You will hear it pop. 
With your knife, cut through the joint. This is your thigh and drumstick. 
You will see a line right between the drumstick and the thigh. This is a free arrow that points and shouts "Cut here!". 
Cut through the joint. 
Repeat to the other thigh and drumstick.
Make a slight diagonal cut right next to the chicken wing. Probe with your fingers first and find the joint, so you'll know where to cut. It should cut clearly through.
Repeat with the other chicken wing. 
Use sharp kitchen scissors to cut through the rib cage around the chicken breast. 
Cut the chicken breast in half. This bone is really strong, so you'll definitely need a sharp knife. You may also wish to cut each chicken breast half in two.
Save the chicken backbone and use it next time you make Chicken Broth. It's really very simple. Start practicing:).
Thanks! This is very helpful!