Place the chicken on a cutting board, pat dry with paper towels and place it breast side up.
Start cutting where the leg attaches to the breast, then pull away the leg from the breast and cut through the skin. Now pull away the leg with a little more force until you pop the joint (hip bone) out of its socket then cut away at the joint. Repeat on the second leg.
Flip the chicken to one side, and locate the joint (not the bone) where the wing is attached to the carcass. Pull the wing away and cut through the joint to remove it. Repeat with the second wing.
Flip the body over, then using kitchen shears cut through where the back and the breast meet. Remove the backbone and save it for stock.
Flip the breast over skin side down, and find a white thin line in the center. That's the cartiladge and exactly where you need to cut. Cutting through it will separate the breast.
If you'd like to cut the breast into smaller pieces (this will help the breast cook evenly with the smaller pieces of chicken such as the thigh and drumstick). Flip the breast over, skin side up then take your chef's knife and cut through the breast almost in half (the thicker part must be a little smaller than the thinner side).
If your recipe calls for leg quarters, then skip this step. If you want to separate the leg, find the white fat line running between the drumstick and the leg and cut through it. Make sure that you're cutting between the joint and not the bone.