In the traditional peer review process, articles are reviewed before publication by (usually) anonymous experts in the specific topic of the article or journal.
Reviewers judge the quality of the article by addressing the validity of the research, whether or not the methods chosen address the question(s) asked, and the accuracy of the data.
Journals can reject a paper if it does not meet the reviewers' standards; more usually they will ask the author to address any questions, problems or gaps identified by reviewers, revise the article and re-submit it for review again. This can be a long process and usually takes at least 6 months or more. Very current events will likely not be addressed by peer-reviewed articles.
Peer-reviewed articles are also sometimes called scholarly or refereed.
Use a database to search for articles by topic. Many databases have an option to limit search results to only those that are peer-reviewed.
These filters limit results to items published in a peer-reviewed journal, it does not always mean every individual item has been peer-reviewed. Usually only original research articles are peer-reviewed; not book reviews, commentary, letters, news, or opinions - these may still show up in search results when a peer-review limit is used.
The publisher's website for the journal will often contain the words "peer-reviewed" or "refereed". There may also be instructions for authors that describe the review process for submitted articles, the percentage of articles accepted, and the average length of time the review process will take.
The database Ulrichsweb can be used to check if a journal is peer-reviewed, but remember it is just a tool and you should still examine the journal closely if you are not familiar with it.
Enter the journal title (not the article title) in the search box. Click on the title from the results list and look for "Academic / Scholarly" in the Content Type field and "Yes" in the Refereed field. If there are a number of journals with a similar title you may need to use the ISSN number to find the correct one.