Hey! It's super easy ! Just find the nearest consulate near you and make an appointment online. You should request a limited validity passport of 2 years for your baby. You can email the consulate to see what exactly they want. I had to bring my wife, our daughter, our marriage certificate, wife's national ID, baby's birth certificate, the photos (with req. info on back one ONE copy, other copy blank), my Canadian passport and I even brought my drivers license because they like extra ID. All non-English documents have to be translated and you should have the translator stamp the translated docs with so they supply their name and the name of the company. Our marriage papers were notarized, which is even optimal.
The passport will come in about 6 weeks and the citizenship certificate will come in about a year. (note: I sent baby's citizenship certificate to my dad's place in Canada because in a year we should be there. You can send the passport and citizenship cert to different addresses)
Hopes this helps ! Make sure to looks online for photo details and exactly what to bring. And definitely don't forget the wife and the baby when you go to apply !!
Oh yah, if you put a Chinese name on the birth cert then they will put it on the passport and citizenship cert (in pinyin).