Peer review is a process by which scholarly work or research (often articles) are subjected to evaluation by other experts on the topic. Reviewers judge the work by its originality, accuracy of information, importance to the field, research methodology, and other criteria to determine if it is worthy of publication. Peer review is also sometimes called "refereed".
Scholarly is a broader category, that includes peer review and review by editors who are experts in the subject. Both are very different from regular magazine articles which are usually reviewed by a professional editor who isn't an expert in the subject.
The simplest way to find a peer-reviewed article is to use a database helps you search for peer reviewed journals.
Look for a check box near the search box for Peer-Review or Scholarly Journals.
This will limit your search to articles in scholarly journals, but not necessarily to the research articles in those journals. To find only research articles:
Some of the databases that have Scholarly/Peer Reviewed check boxes are:
Some databases are entirely or almost entirely scholarly journals. Any research article you find in a purely scholarly database will be either peer reviewed or reviewed by an expert editor. (You still need to watch for news, opinion, and commentary articles.)
Some of the scholarly databases includes:
If you have an article already and want to know if it was published in a peer reviewed journal, you can look that journal up in Ulrich's Periodical Directory. Look up the journal title (not the article itself). Ulrich's uses "refereed" instead of "peer reviewed".