If you are looking for a specific journal article and have a reference to it (e.g. from a bibliography or reading list) use the Library catalogue to search for the journal TITLE. The catalogue will tell you if there is a print or electronic copy of the journal available from Durham University Library.
If you are looking for any articles on your chosen subject, you will need to use bibliographical databases for your subject to search by keywords. These will list articles that match you search criteria. You can either open the article directly (if the Library subscribes to the journal) or go to the Library catalogue to search for the journal title