Start at the library homepage and click the Journals, Magazines, & Newspapers link under "Find." Type the full journal title in the search box there (don't abbreviate and don't skip things like "Journal of"), and click Search.
Scan the list of results to find a database that contains the dates that you're looking for (e.g., the one marked "from 1997 to present" would not have that article from 1980). Click on the database name to get to the journal. If you are off campus, you may be prompted to log in with your A-number and Banner password at this point.
Once on the journal's website, you can usually browse through its issues by year or use their search feature to search for a title, author, or topic.
Additional information can be found on our e-journals libguide.