There are two ways to do this. One is to Google the journal itself and look for a link to the current issue. Generally, you will get something like this http://ajs.sagepub.com/content/current. You won't be able to see the whole article but there should be a link to the abstracts. Once you find articles you want then do an ILL - we generally get things the same day.
A second option is to do pretty much the same thing in PubMed (see image below). Hit the Advanced link under the search and then type (DO NOT COPY AND PASTE) the name of the journal and let PubMed help you get the exact title - for instance you have the THE in The American Journal of Sports Medicine for this to work. PubMed does a last in first out default results display so the most current will be at the top of the list. If you use the PubMed route you will get the red article linker button that will lead you to our Interlibrary Loan page.
Google is easier but the red button auto populates the ILL form for you. And don't forget to see if we have a subscription by using the Journals tab in the center search box on the library homepage.