Upon acceptance of a Staatsangehörigkeit § 5 declaration, making one a German citizen, the next step is generally to order a German passport called a Reisepass. This requires filling out the form and bringing the Urkunde über den Erwerb der deutschen Staatsangehörigkeit durch Erklärung and passport photos to the responsible Consulate in a passport appointment.
It can be difficult to get a passport appointment. You keep checking the site and there are never any appointment slots available.
German Consulates around the world add new appointments every weekday at midnight in Germany. For example, that is 3pm in California. If you start polling the appointment site at 2:59pm on Sunday, you have the best chance of seeing new appointments appear and grabbing one before they are all gone. Note that Daylight Savings Time differs by several weeks between Europe and the US, they aren't the same number of hours apart all year.
There are Honorary Consuls in a number of cities who can make copies of your documentation and forward it to the Consulate, which might be easier to get an appointment with if your Consulate is swamped.