The simplest way to integrate Moodle and Zotero is to create a "smart reading list". You copy-and-paste your Zotero bibliography as HTML into a Moodle web page or label. Students can then capture the references into their own Zotero libraries. When they visit the Moodle resource they will see the familiar "Save to Zotero" icon in the address bar.
If you are using a Zotero group students can join the group, synchronise with the group library and even add their own readings. You could publish the group library dynamically within Moodle as a simple web page or, using the group's RSS feed, as a Moodle RSS block.