Our catalog and many of our databases have a check box you can use to limit your search to peer-reviewed journals. 
In some databases it is labeled "Scholarly Journals", "Academic Journals" or something similar.
But be careful! Not everything published in a peer-reviewed journal is a peer-reviewed article!
So, how can you tell if an article is peer-reviewed? And what is peer-review, anyway?
For a quick explanation of peer-review, take a look at the video at the end of this answer. It is a very good, very quick explanation from the librarians at North Carolina State University.
The important thing to know is that these articles are the way researchers share their research with other scholars (including you!) So, if the article is in a peer reviewed journal, and is presenting the results of the authors' research, you can be confident that it is a peer reviewed article.
In the sciences, these articles will often will have methods and results sections. In the humanities, it can be harder to tell at a glance. But, watch out for book reviews, editorials, or other types of articles that aren't presenting the authors' own research. These are usually not peer-reviewed even if they are published in a peer-reviewed journal.
Sometimes it's hard to tell if an article is peer-reviewed or not. We can help! Call, chat, text, email, or stop in and talk with a librarian.
Here's the video that explains what peer review is:
