I reside in the US and I have a green card. How do I apply for a visa to China?

Farai, you can follow the steps below.
First, collect all documents that may be required, such as your passport, a copy of the passport's first page, an application form, a passport-sized photo, the original and copy of your green card, and proofs justifying your purpose of visit.
Then, go to the embassy or consulate which has jurisdiction over your residence to submit the application.