The quickest way to tell if a journal is peer reviewed is, if you have an article title or journal title, to search the catalog. This icon next to a result will tell you if it has been flagged as peer reviewed or not:
Journal publishers should say on their websites whether articles go through a peer review process, but it can sometimes be hard to find that information if you're not sure where to look. Sometimes websites go down, publishers go out of business, or any other number of factors could keep you from being sure.
Another quick way you can find out whether a journal which publishes refereed, or peer reviewed, content is using the database Ulrich's Web. That link directs you to a url with our proxy, which will prompt you to log in for access. TCC subscribes to Ulrich's Web.
Once in the database, search for the journal title. Journals that are refereed or peer reviewed have a black and white striped "referee shirt" icon next to their name in your list of search results.