Read current or older issues of a scholarly journal find Browzine 
(from web) or Find a Scholarly Journal from Research Tools drop down menu (library website).
From the Browzine site, FIND JOURNAL BY TITLE, SUBJECT, OR ISSN or BROWSE BY SUBJECT
The most current issue's articles are displayed by default. On the far left side of the page, you'll see links to the available past years.
View Tutorial < 3 minutes in length
Underlying the page is the availability/coverage information for the database(s) indexing that journal title you typed. Scroll down the left side page to find 
click, to be redirected to the Online Journals, Books and more page. Look at the date range by database to know much of the journal has full text coverage in that database.