As of version 6, Zotero has its own built-in PDF editor that can be used to annotate PDFs. If you use another program to edit PDFs, Zotero will still save the annotations you make from PDFs in other programs, such as Adobe Acrobat.
To enter Zotero's PDF editor, double click a PDF or the reference that the PDF is attached to.
Clicking the button in the top-left (left of the magnifying glasses) will show a list of all the annotations currently in the document. There are many different annotations you can make:
Zotfile is an open source plugin for Zotero that can automatically extract annotations and save them in a Zotero note. You can use this to keep track of quotes you wish to cite, or important ideas to remember without opening the PDF directly, but Zotero 6 aleady does this. Zotfile can also be used to automatically batch rename and move attachments, and sync PDF's with a tablet.
If you want to edit Zotfile preferences, they can be found under "Tools > Zotfile Preferences..."