Registration of Birth of child in Germany

The hospital where the birth takes place will record it and give you some paperwork  to submit to the family registry ("Standesamt") within a certain time (one week if I remember correctly), together with the birth certificates of both parents and their marriage certificate, if applicable (all documents must be submitted in original!).
Many maternity hospitals have an office of the family registry on site, so you can start the procedure right there.
After a certain time of processing (which can be weeks) you will be issued birth certificates for your newborn, which you can then use to apply for passport, Kindergeld, Elterngeld, health insurance, etc.. For an extra fee, an international birth certificate in English can also be issued.

I am not familiar with the requirements for notifying your consulate or embassy of the birth. You should call them to ask.

Thank you Beppi.Do you know if the marriage and bith certificates of the parents has to be translated into german or is english ok.

They have to be officially translated by a certified translator.