When? Start immediately. Yes, immediately start introducing these words to your child.
How? The simplest way is to start saying these words while you dress them. Such as, "Left leg" while you grab their left leg to put on their pants, "Left foot" while grabbing their left foot, "Right arm", while putting their arm through a sleeve, "Right cheek" while giving them kisses on their cheek. The one side is typically followed by the other side. And yes, often you'll just say foot, and that's ok. But you'll want to start this as soon as their born. Yes, they'll get it later in life, but teaching early is helpful for them and you, and if you start right away, it helps put you in the habit for when they really start soaking it in.
Why? It's part of getting a jump start on their intrapersonal awareness. Before Joey was two, he was well aware of his right from his left. When he started riding his bike, he was much more aware of looking left and right to make sure no cars were coming. When he drops something, I tell him that's it's next to his left foot and he finds it more easily. When we practice sports - soccer, t-ball, football, etc, it makes more sense to me to tell him "ok, now try throwing with your right arm," instead of using the word "other" for everything.
In the Long Run: Granted, there are plenty of adults who don't know their right from their left and live just fine, but I think knowing makes the process a lot simpler. And yes, this is a left brain function, but as a parent, any little bit to make their journey a smoother ride, I'm going to try to do. Hope that makes sense.