The fact that we now roast a chicken almost every week has helped, although my poor husband had to listen to quite a bit of swearing over the last few years as I struggled to teach myself. The thigh was always my nemesis. Wing, drumstick, no prob. But the thigh was always tricky to outline and inevitably I ended up hacking into the joint, either resulting in a very tiny thigh or a weirdly large one carrying with it part of the bone that connects the thigh to the back I guess (do chickens have hips?).
Anyhow, I finally figured out a few things that really make it easier. 1) Let the meat rest. I knew this from a cooking standpoint--let the juices redistribute etc-- but letting it cool makes it much easier to handle and the parts become more distinct. 2) The order that works best for me goes: drumstick, breast, wing, thigh. And here's the secret with the breast: remove the entire breast off the bone, which is easy, but takes a bit of practice so you don't lose much of the meat, then slice cross-wise. I used to just slice it straight off, but I have to say, not only does it end up looking much prettier, but the cross-cutting makes for more tender chicken. Slicing it straight off results in unnecessary shredding. 3) Do not cut into the thigh until you find the joint. This is basic, I know, but it has generally been a problem for me, as I would get frustrated and end up angrily hacking through something or other just to get it done. But if the chicken isn't too hot and you're careful, you can find the joint and remove the thigh so it turns out intact.
I should have taken a picture of the chicken cutting procedure but juggling the chicken, knife, and camera seems tricky. The husband has been interested in helping me with the picture taking business so next time I will enlist his skills.