When you download Zotero, it automatically adds a Zotero toolbar to Microsoft Word or LibreOffice.
If you don't see the Zotero toolbar, try to reinstall it: word processor plugin troubleshooting.
From the "Zotero" tab in Word, you can add citations while you write:
When you click "Add/Edit Citation" you can search all your Zotero references by author or keyword. Select the one you want and it will insert a citation:
Once you're ready to create your bibliography, just click "Add/Edit Bibliography" and Zotero will create a list of all cited references: