Yes, thanks to the Shepherd breeders who have managed to about ruin the hips in the breed, most show dogs now look like they ate down on hocks. :-(
Anyway, your worst enemy is the weight issue so you really need to get the weight off with a weight management food, the green bean diet, etc and maintain it. The dog still needs moderate exercise to maintain muscle tone and strength. Try to avoid stairs, jumping, etc. aquatic therapy is great if you have a pool or facility near you for rehab (hard to find). As Ellen said, Glucosamine is good but it may take 4-6 weeks to see any benefits. Check with your Vet on the dose. Anti-inflammatories are often used but one may work better than another. Watch kidney/liver function on these meds.an orthopedic bed is a good idea. There is something called a hip hammock that can be very beneficial for a dysplastic dog. Of course, there is always some type of surgery which can be extensive and expensive. If you have a Vet school near you, you might want to contact them.
First and foremost, you need to get the dog down to a decent weight.
Good luck.
Oh and maybe antiinflammatories for a short time to help your dog become mobile.
I'm not sure about what surgery odds are. Does your vet think that joint supplements, weight reduction maybe with a special food at first and then gradual excercise would help? I know things like glucosamine and missing link can be helpful. I also believe German shepherds are prone to hip dysplasia if I remember right. An orthopedic bed and keeping your dog sleeping indoors may also help.