This is partly a question about identifying sources, as the peer review process is a characteristic of scholarly (or academic) journal articles. Research articles published in scholarly journals are usually peer reviewed. The only items published in a scholarly journal that are not going to have gone through peer review will be letters to the editor, editorials, book reviews, and the like.
However, on occasion you will also come across a scholarly journal that does not use peer review, or you might also want to make sure about the peer review status of a publication. One good method is to check the publication information in Library databases. For example, Academic Search Premier and other EBSCOhost databases as well as those from ProQuest include publication details for every journal, magazine, newspaper and other source they list in their collections.
Note that your list of search results will include icons that indicate the type of document, as seen in the image below:
When you have clicked into a document, pay attention to identifying characteristics such as the title and abstracts to learn more about the document. While these characteristics are helpful in figuring out whether you've found a peer-reviewed source, you can also click on the publication title for more details about the journal, including peer review status.
Similar to EBSCOhost, ProQuest gives you a descriptor to help identify source type, as well as links to more information about the publications.