One of Zotero's best features is its ability to write citations and create bibliographies.* The Zotero menu will automatically appear in your Google Docs editor after you install Zotero.
*You are responsible for proofreading any of the citations Zotero generates for accuracy.
Place your cursor in your document where you want the in-text citation to appear. Click the Add/Edit Citation button in the menu. If you have not already done so, Zotero will ask you to choose a bibliographic style for the document. Your selection will affect all citation and bibliography entries added through the Zotero plugin. It will not affect citations typed in manually. You can change the bibliographic style later by clicking the Document Preferences button.
After clicking Add/Edit Citation you can find a document from your Zotero library by typing in the red search bar. You may search by author, title, or any other information from the item record. You can also browse the library by clicking the red "Z", then selecting Classic View.
When you are finished writing, you can insert a bibliography by clicking the Add/Edit Bibliography button in the Zotero menu. This will create a fully formatted, alphabetical list of any references you have added to your document using the above method. Any citations you add after inserting the bibliography will automatically be added to the list as you work.