1. Legs and Thighs: Begin with a very sharp boning or chef's knife and a carving fork or long two-pronged fork if you have one. Lay the chicken breast side up. Make a slash through the thigh where it's tucked up against the breastbone, pulling the leg away will reveal a nice separation that doesn't even need cutting, just pull gently. At the bottom will be the joint, that you have to confidently yank on, or insert the point of the knife into the joint, then pull down, it should snap and you peel away the leg. The leg and thigh are still connected to each other. You can separate them easily by finding the mid-point joint and slicing.
2. Breasts and Wings: To carve the breast meat, first put your fork through the back to stabilize it on the cutting surface. Find the keel-bone, which runs across the very top of the chicken, when it lays breast side up. Slice just to one side of the keelbone, right along the rib cage, coaxing the hunk of breast meat away with the blade as you slice and gently rub the blade of your knife along along the rib cage. At the bottom there will be another joint to separate. The breast will have the wing attached that you can easily remove, if desired.