Common courtesy is what it all boils down to. There is no one "rule" to work off of all the time. Every course has a different feel. Know where you are before you let them run free. What works at one course may not be kosher at all somewhere else. Just like you get layered up to go play in inclimate weather, same goes for golfing with your dog. Have certain items for their maintenance:
1) Leash (mando on some courses, Just In Case on others)
2) Poop bags (any will do, some parks provide em, use your beer bag if you have to)
3) Water (dogs get thirsty too, not all courses have H2O)
4) Treats (one way to keep them close is to reward them for doing so, and in case they beg for someones beef jerky)
5) Toy (This could be a ball, their own disc or even just a stick)
I also recommend feeding them before going to the course, so they will not be as distracted by their belly while you are out there.
Just respect the people around you and the level of dog interaction appropriate for your course.