The quickest and easiest way to verify if a journal is peer-reviewed is to look it up in Ulrichsweb, a database that provides bibliographic and publisher information on all types of serials (journals, magazines, newspapers, etc.).
Once you've looked up the name of a journal, look for a referee’s jersey icon next to the journal’s title on the results screen. The referee jersey icon indicates that this journal is refereed/peer-reviewed.
Please note that Ulrichsweb will not lead you to the full text of any articles.