I just did the authentication of my son's birth certificate who was born in
New York in the Chinese embassy. Here is the steps,
step1, go to the health department(125 worth street 1st Fl 9:00-3:00,212-788
-4500), ask for a long form and a explain letter. They will mail you in 2
weeks.
step2, when you got the long form and the letter, go to the county clerk(60
centre stree room 300), ask for the notification of the document.
step3, after you finished in the county clerk, go to State office(123
wiliman street? not very sure this address, you can ask the county notify
public), get the notification of the document.
step4, Copy all your document before you go to the Chinese embassy, be
careful do not tear or depart the document you got from the state office.
when you get to the embassy, line in the area which people apply visa(window
3-5?, 1st Fl), in 4 days, you can pick it up.
Just a suggestion, if you want to use these documents in China, why don't
authenticate the translation of the birth certificate? you can translate by
yourself and the procedure is almost the same as you do for the birth
certificate except step 1. You can translate the certification by yourself,
and then get a local notify public ( you can find one in your bank, it's for
free) to notify it, but make sure the notify public must got her license in
the same County as you will go on step 2), the next step are the same as
above. You can do these at the same time.
Regarding the marriage certificate, I don't have any experience, so I can't
have any suggestions.