I am a United States residen with a green card and not a citizen yet.

Tonia, if you want to apply for a Chinese tourist L type entry permit, you should first prepare the required documents containing your passport and its copy, the application form, a passport-style photo, your green card in US, round trip air tickets and hotel reservation, as well as other documents required by the consular officers. Next, submit the application to the embassy of China to apply for it.