I am going to be getting a service dog soon and my apartment has a no pet policy. I know that my service dog will be exempt from this but what kind of proof do I need to provide my apartment manager with?
A service animal is NOT a pet. They are not viewed as pets by any governmental agency.
If the restaurant says no pets, you can bring in a service dog. They cannot object under ANY means. The animal is not a leisure "pet". It is a "duty" animal that has task/s to perform. You have the LAW and disability rights on your side.
You will need Training Certificate that shows the dog has been trained for (whatever services it is to do). When ON duty I HIGHLY recommend having the dogs wearing a "vest" (colored) so it does not appear to be a "pet". That will also give you a location to apply the certification patch and any ID you want. Dogs wearing vests people tend to not approach. Dogs also can learn (or be trained) that Vest means "on duty".
If there is a canine training center (or where yours was trained) in your region they can help dealing with rental questions and smoothing over any questions management may have.
I sit on the board of a condo association. Our building has a "No Pets" policy, but we are required by law to allow service animals. What we require is a signed letter from a doctor, on his/her office stationery, stating that the animal is needed to provide a service. We have a resident who has a small dog "for emotional support", so I think you'll be okay ;o)