It's easy to add PDFs to your Zotero library and automatically import their citation info.
First, enable PDF indexing on the Search tab of Zotero's preferences (found by clicking the gear icon). Zotero will download and install a small plugin.
Next, just drag your PDF files into the Zotero pane.
Right-click the PDFs and choose "Retrieve Metadata for PDFs." Zotero will retrieve their citation data from Google Scholar and turn them into citeable items with PDF attachments.
You've probably seen the 
button in some article databases that allows you to locate the full text of an article online. See how here. Zotero allows you to use the same feature.
To set up Zotero to access the Article Linker server, click the gear button on the Zotero toolbar and choose Preferences, then Advanced, At the bottom of the preferences window, paste this url into the "Resolver" box: http://zc6sj2ch8l.search.serialssolutions.com/?id=
Then click OK. Once you've set this up, you can click the Locate button on any citation you're viewing to search for the item online.
When you have downloaded the PDF, just drag and drop it onto the Zotero citation.