Using Zotero with Google Docs is similar to using it with Microsoft Word. There is a Zotero drop-down menu where you can add a citation, add a bibliography, and change the citation format of your document. The first time you do this, you'll need to link your Zotero account with your Google Drive account.
1. To add a citation, place your cursor at the end of the sentence where you want to add a citation. Click on the Zotero menu and then click on Add/edit citation. Alternatively, you can click on the Z icon on the toolbar.
2. In the pop-up window that comes up, click on your preferred citation style, then click OK.
3. In the red box that comes up, type in part of the title or an author for the paper you want to cite. Select the correct paper from the dropdown menu. Press Enter when you're done.
4. That citation is now in the document where your cursor was.
5. After you've added the rest of the citations in your document, you can add a bibliography. Put your cursor at the end of the document, then click on the Zotero menu and then Add/edit bibliography. A bibliography, formatted in your chosen citation style, is added to your paper.
6. To change the citation style, click on the Zotero menu, then Document preferences. Click on your preferred new style, then OK. The resulting document will be formatted according to the updated citation style. Here, I've changed from APA to IEEE.
For more information, take a look at the Zotero support page about using Zotero in Google Docs.