I carry a few different ways. The speed and distance I'm walking, plus the amount of photography I plan to do, decides which one to use.
If I expect to take frequent photos while walking, I repeatedly loop the strap around my right wrist to take up all the slack and carry the camera in my hand. It's ready for instant shooting.
If I'm not walking very fast and want to keep both hands free, I hang the strap under my left arm and around the right side of my neck. This takes up most of the slack so the camera doesn't bounce much. As I walk faster I keep my left hand on the camera to prevent bouncing. I can easily slide my left arm through the strap to get the conventional around the neck position for shooting.
The camera goes in my bag when I want to walk fast and not take many photos. My favorite bag is LowePro Slingshot 100 (a tiny bag yet enough space for a K-5, 55-300, 16-50, and 10-24 or several primes) because it swings to my chest for easy camera retrieval. If more storage space is required then I use a large backpack that must be removed for camera access.
---------- Post added 11-02-15 at 12:39 PM ----------
Originally posted by csa Well, it varies with individuals as to what they can comfortably take on a walk. I take my 55-300 lens that covers just about anything I would come across to photograph. I'm 74, and I'm lucky just to be able to take walks, without taking "luggage" with me!
In that case, let me amend my comments. You probably aren't walking extremely fast, so my 2nd option of sliding your left arm through the strap for a diagonal carry is probably best. That assumes you don't have any shoulder issues that make the maneuver uncomfortable.