Peer-reviewed articles are published in peer-reviewed journals.  So, to verify if an article was peer reviewed, you must see if the journal it was published in is peer-reviewed.

UlrichsWeb is a great tool to use to find out if a journal is peer-reviewed.  UlrichsWeb is a directory of periodicals, so you can use it to find out information about newspapers, magazines, scholarly journals and other information sources that come out periodically.  

To get to Ulrichsweb, start on the library's homepage.  Click on the 'Databases" link underneath the Compass search box. In the "Databases" search box, search for "Ulrichsweb" and it should take you to the database entry  Click on the name of the database, if you are off campus you will need to log in with your DU credentials.  

Once in the database, search for the name of a journal.  

Choose your journal from the list of results:

You can find out all the details of this publication on the results page, including if it is peer-reviewed, or referred, or not.  It will have a yes and a referee jersey icon indicating that the journal is peer-reviewed: