Do you know the name of the journal you want to access? On the library's homepage, select the "Search for Journals" tab to find a specific journal title.
The simplest way to find a peer-reviewed article is to use a database helps you search for peer reviewed journals.
Look for a check box near the search box for Peer-Review or Scholarly Journals.

This will limit your search to articles in scholarly journals, but not necessarily to the research articles in those journals. To find only research articles:
Some of the databases that have Scholarly/Peer Reviewed check boxes are:
This multi-disciplinary database provides indexing, abstracts and much full text for academic journals, magazines, trade publications, and newspapers on every topic.