If you have Word open when you downloaded the Zotero desktop application, the Zotero toolbar may not display. Close Word and re-open it. If the toolbar still doesn't display try going to your Preferences and install the add-in manually. Click the Cite tab, then the Word Processors tab.
Boston University Law Library has a guide for using Zotero with the legal databases LexisAdvance, WestlawNext, & Bloomberg Law.
Additionally they list a number of useful tools for organizing and citing your research.
Georgetown Law Library also has some tutorials and recommends a Zotero variation called Juris M.