For bone-in chicken breasts:
starting at the tail of the bird, using a boning knife - slice up each side, thru the cartilage where the ribs come together all the way to the "armpit"; lay the bird open. Slice thru the sholder joints, giving you two halves of the bird: breast and back.
I do not cut the wishbone seperately.
Lay the breast half skin-side down on a towel over a cutting board (or non-sliding matting of some kind), shoulder end away from you.
There will be a "valley" across the top of the breast, place your knife there, and slice toward you thru the cartilege to the keel bone.
Turn the breast around, with shoulders toward you. Reposition the knife into the cut you just made; cut down to the skin, thru the wishbone.
Turn the breast again, shoulders away from you. Grasp the breast in both hands, one holding each rib-cage; Fold the breast in half away from you (skin-sides together), until the keel bone "snaps" and starts to pop free.
Lay the breast on the cutting board; place "off hand" (left if you are right-handed, right if you're left-handed) over the wish-bone area, and pull the keel bone out.
Take a sharp knife and slice thru the skin and any uncut flesh where you just removed the keel bone.
Voila! Two breast halves! I've got this down to where I can fully cut a whole chicken carcass in about 8 minutes.
For slightly larger breast pieces - instead of cutting up the sides of the chicken, I cut parallel to the spine on both sides, from "waist" to neck, wherever the meat on the ribs thins out to "not worth the effort to eat"; usually close to the spine.
Backs, neck and wing tips go in the stock pot. Once I have "home-grown" birds for the table, the feet will go in the pot as well. I've been told that it gives a good golden color, better flavor and gelatin to the stock.
BTW - save your bones after dinner. You can still throw those into the stock pot, and the double cooking gives you a deeper color, and more intense flavor.