Most research databases allow you to limit your results to articles published in peer reviewed journals. Usually there is a checkbox labeled “Scholarly or Peer Reviewed Journals” - or, in some cases, "Refereed". Check this box, enter your search terms and click search. The results should all be peer reviewed.
If you retrieved your article electronically, either through a library database or Internet search engine, you can use Ulrich's Periodicals Directory to determine if the journal is peer-reviewed.
Go to Ulrich's and do a Title Keyword Search for the name of the journal in which your article appears. Locate the appropriate listing and click on the journal title. In the 'Basic Description' tab, look for the heading 'Refereed', with an indication of yes or no. If you do not see the Refereed field, look for the Document Type field, which indicates if it is an Academic/Scholarly journal or a Trade or Consumer (Popular) magazine.
If you are getting your article directly from the printed journal (and not through an electronic database), it should indicate whether it is peer reviewed. Check the front material where the journal describes its own policies.