I have always let my dog go potty off leash in her own backyard, but what I have done most recently is fence off a portion of the yard and designated that her "Potty Area". I most recently did this because we have an Agility Course set up in the yard and she (or any other dog) is not allowed to pee or poop on the course. They have to potty in their designated area.

I, however, always go out with her and when she does her business...I cheer, jump up & down with excitement (my neighbors think I'm looney, I'm sure), and praise her with "Good PeePee" or "Good Poo".....This has taught her to pretty much Pee & Poop on command, both either on or off leash.