Installing the Zotero desktop version should automatically add the Zotero plugin to Microsoft Word. Once in a while it doesn't work. After downloading and installing, check your MS Word toolbar: is "zotero" there? If so, great! If not, first try quitting MS Word and rebooting your computer. If it still doesn't appear, check this Zotero documentation about how to correct the problem.
This guide is adapted from one originally created by Jason Puckett and licensed by Georgia State University Library under a Creative Commons Attribution-NonCommercial 3.0 United States License. Jason's original guide is also available online.