You will never find a scholarly journal at a news stand or in the grocery store. The publications you find there are always either general/news publications or popular magazines. Scholarly journals are bought by subscription straight from the publisher. To find them, you must either visit the library or use a database.
If you visit the library, staff at the information desk can help you find scholarly journals.
Usually, the most convenient way to find scholarly journals is through a database. Some databases like JSTOR or ScienceDirect College Edition are aimed at scholarly research and contain mostly scholarly journals.
But what if you don't know which database to use or how to start your search?
A good place to start your search for scholarly journals is VanguardSearch. It will allow you to search all of the library's online databases and then refine to scholarly & peer reviewed journals. You can find more information on how to search at https://libguides.asub.edu/VanguardSearch.