To find out if a journal is considered Refereed/Peer-Reviewed, check the Ulrich's database by doing a search for the title of the journal. In case Ulrich's does not list a journal, another database that can also help with this is Serials Directory.
Many, but not all, of the research databases accessible from the Library allow searches to be limited to articles published in Scholary/Academic as well as Peer-Reviewed journals. If a database only has a "Scholarly" or Academic limiter/filter, keep in mind that refereed/peer-reviewed journals are a subset of scholarly journals, in other words not all scholarly journals are refereed/peer-reviewed.
To view a tutorial on what makes a journal scholarly, please see this tutorial from Rutgers University.
Most libraries subscribe to various types of periodicals, such as scholarly (some of which may be peer-reviewed), popular, or trade publications. Choosing which to use depends on your topic, the type of writing you are doing, your assignment, and the sources your professor wants you to use. Many databases offer the option to limit to "Scholarly Journals" or "Peer Reviewed". If you're not sure if a journal is considered scholary/peer-reviewed, check Ulrich's by looking up the title of the journal.
Examples of scholarly journals:
What is a peer-reviewed journal?
A scholarly journal is peer-reviewed when there is an editorial board that decides which articles should be included for publication. These journals are generally thought to be of the highest quality. To determine if a journal is peer reviewed, look for an editorial board in the early pages or on the journal's Web site.