You can import bibliographies and libraries from other apps to Zotero, as well as RIS files that you might export from Ovid, Medline or other reference managers.
To do so, click "File" in the top left of Zotero, then "Import". From here, choose to import from a file or via Mendeley; in the former case, select the file and all citations included will be added to your Zotero library.
There are several alternative ways to save citations to Zotero if the Connector is unavailable or uncooperative. The easiest of these is adding by identifier.
To add by identifier, click the magic wand icon in Zotero
In the entry that pops up, enter an ISBN, DOI or PubMed ID and press enter. Zotero will automatically retrieve information about the reference and save it to your library. This will not save a fulltext PDF, but will link to the webpage where the citation is available.
Adding by identifier is useful when gleaning citations from a reference list or bibliography - instead of searching individually for each item, you can copy in the DOI or other identifier and save the citation immediately. It is also useful for adding physical titles to your library that you might want to cite later - enter the ISBN number and the relevant item will be automatically added.
If you are unable to save a citation by the methods above, you can manually add a reference. This is a more laborious process, as you will need to fill in the bibliographic information yourself.
To add a reference manually, click the Plus icon in Zotero:
Choose a category that best fits the item from the list - you can find additional categories under "more". From here, you can fill in information about the item in the "Info" tab to the right of your library. If you want to attach a file, you can drag and drop a file into Zotero. You can also right click on the item and click "add attachment".