When you install Zotero on your computer, it will automatically install a plug-in for Microsoft Word. In most cases, this will appear as a Zotero tab. If you have an older version of Office, check the "Add-ins" tab.
This menu allows you to
add citations or edit existing citations to your document,
add a bibliography or edit the existing bibliography,
change the citation style of the entire document in "Document Preferences,"
refresh the document so that any changes made are reflected (such as editing a citation in your application or adding a new citation to the document after adding the bibliography), and
unlink the citations, which removes the Zotero fields and just leaves the text of the citations.
To add your first citation, put your cursor where you want the citation to go and click the "Add/Edit Citation" button.
If you are working in a new document, the first time you go to add a citation a box will appear prompting you to select the citation style of the document. You can always change this later! This comes in handy if, say, you submit an article to a journal and it gets rejected. You decide to submit it to another journal, but they use a different citation style.
After clicking "Add/Edit Citations," a red search bar will appear on your screen. Here you can search for the reference you want to add using any keyword, title, or author. References in your Zotero library as well as references already in your document will appear.
In the results list, select the reference you want to cite. In the search bar, a preview of the in-text citation will appear. If you need to add a page number or suppress the author, click into the citation bubble and a menu box will appear.
If you need to add more than one reference to a citation, repeat this process by putting your cursor back into the search bar.
Press "Enter" on your keyboard to insert the citation into your document.
When you are ready to insert your bibliography, again place your cursor where you want the bibliography to start and click the "Add/Edit Bibliography" button. Your bibliography will automatically generate according to the references in your document and will be formatted according to your citation style.
Sadly, at the moment, there is no official Zotero to Google Docs plugin. However, using Zotero with Google Docs is incredibly simple!
When you want to add a citation, go to the Zotero Library and right click on the reference you want and click "Create Bibliography from Item."
You can also hold down the shift key and drag the reference where you want in your document.
After you select "Create Bibliography from Item," select the style of your citation and select "Citation" under "Output Mode." For "Output Method," select "Copy to Clipboard." Then paste into your document where you want your citation to go.
When you're ready to create your bibliography, select the references you used by doing Control+Click or Shift+Click. Then right click and again select "Create Bibliography from Items."
You can also drag the selected items into your document after selecting them all, and it will still keep it formatted to your citation style; just make sure your preferred style within the Zotero application is the style of your document.
Tip: Make sure you're keeping track of the references you use, since Zotero will not automatically do it for you! One method is to create a "Citations Used" folder or subfolder in your library and add your references to that folder as you put them in your document.
After right clicking your selected items, again the Create Bibliography menu will appear. This time, select "Bibliography" instead of citations. Then paste your bibliography into your document.