Can you please tell me how I can obtain German birth or death certificates?

Records regarding birth, death and marriage are normally kept by the Standesamt (the municipality offices) where the event occurred.

Most cities have websites at www.(nameofcity).de where you can find the contact information for the appropriate Standesamt. The request for the birth or death certificate should be done in writing and contain as much information as possible, including proof of your identity and your legal right to obtain the document.

Another option is to contact the nearest German Consulate for assistance. In order to find your nearest consulate go to the appropriate consulate/mission for your country:
US – http://www.germany.info/Vertretung/usa/en/Startseite.html;
Australia – http://www.canberra.diplo.de/Vertretung/canberra/en/Startseite.html;
UK – http://www.london.diplo.de/Vertretung/london/en/Startseite.html;
Canada – http://www.toronto.diplo.de/Vertretung/toronto/en/Startseite.html.

There are also some commercial services on the internet that will help you with this for a fee.