my question: where can i go to get docutment authentication for use in China?

Generally speaking, the birth certificate needs to be authenticated by local Chinese embassy/consulate. Before the authentication, the documents need to be notarized by a local notary public, then be authenticated or certified by the Secretary of the State, then authenticated by the Authentication Office of the Department of State and finally authenticated by the embassy.

For extension, would you mind tell me which type do you want to extend? In general, your valid passport, application form with recent taken photo, your ReigRegistration Form of Temporary Residence for Visitors and some other documents to show your reasons for extension are needed for extension and it can be applied at Exit-Entry Adminstration Bureau in China.