i have lost my passport here in china. how can i find my way home?

Caroline, first, you need to go the police station which has jurisdiction over the plice you lost the airport or the place you stay.

Second, report the loss of your passport to the entry and exit division of municipal PSB. Apply for a "Passport Loss Certificate" from there.

Third, apply for a new passport at the embassy in Beijing. Then apply for a new visa at the exit and entry administration bureau.