Each entry in the Document Vault contains a Preview link over on the right-hand side of screen. If you right-click this link in your browser and elect to Copy Link Address (or whatever the equivalent is), you'll then be able to paste a URL that points directly to the document.
Bear in mind that the document needs to be publicly available if you plan to share it outside of your administration team.
Use the "Update" link to the right of the document when in the Document Vault:
