The PDF reader is part of Zotero as of version 6.0. Double clicking on any pdf stored in Zotero will open it in the reader. You can see quickly which sources have a pdf attachment and which do not:

Double clicking on the pdf symbol will open the pdf in the built-in reader.
There a handful of basic tools for marking up a pdf. In order they are:

These tools create Annotations, which show up in the left pane.
To incorporate Annotations into a Word document or Google doc, they must be added to a Note, which shows up in the right pane.
Click on the next to the last icon on the far right hand side of Zotero to open Notes, then click the plus sign icon where it says "Item Notes" to add new ones.
The Add Item Note choice opens a blank note. Type a note directly into the space OR drag and drop one or more annotations from the left pane into the blank note. To add all the annotations into a single note, choose the Add Item Note from Annotations option.