If you already have some PDFs saved from past research, just drag and drop them from a desktop folder nto your Zotero library. Zotero will automatically search online and match the PDFs with citations if possible. Right clicking or command+click will also produce a menu where you can attempt to retrieve metadata for specific PDFs.

Note: It's likely you will need to edit some entries manually. And, if Zotero cannot harvest metadata from the web, you will need to manually add those citation details.

Believe it or not, you may drag saved bibliography files iinto your Library, and Zotero will do its best to extract and format the source information, Read the easy-to-follow directions in Zotero's thorough documentation.

If you have a basic plain-text document, AnyStyle makes the transfer process simple (see more about half-way down the documentation page)

It is possible to import content from other citation management program accounts into your Zotero account. 

There are more detailed directions for Mendeley exports here and here.