If you have a Word document with citations and a bibliography that you want to import into Zotero, this can be done, but it takes a little work. Zotero has documentation about this on its page about importing formatted bibliographies, and that is the first place to look.
To extract citation information from a Word (.docx) or LibreOffice (.odt) bibliography, try the Reference Extractor. It says of itself that it can "be handy if you lost access to your Zotero or Mendeley library but still have your documents. In this case, you can use Reference Extractor to recover the items cited in your documents, and import them back into your reference manager. Or maybe you received a document from somebody else, and you would like to import the cited items into your own reference manager library."
Download the citations it finds in the suggested CSL JSON format, then import that file into Zotero (File > Import). The citations will be brought into Zotero, but without any PDF attachments. To find them you can right-click on items and select "Find Full Text" and Zotero will do its best. (This will probably work best if you're on campus.)
In the worst case, if the Reference Extractor and all other approaches fail, you will need to add the citations into Zotero one by one, either by looking them up and saving them the usual way, or adding them by hand (with the New Item button). However you do it, if you want the citations to exactly match what is in the source you will need to carefully inspect them by eye and correct any differences.
Zotero's support page has links to all the documentation.
Search the Zotero forums to find answers to common questions, or to submit a "New Discussion".
For more options and answers to common problems, go to our Ask & Services.