If you have access to the article through the library, you will see an Access now button or Access options button below the article on the results page.
You can also limit your search results to full text only by clicking on All filters at the top of the results page and then clicking Available in the library or full text online.
Once you've done that, you should only get results that are accessible through the library databases. If you don't have that filter applied, be aware that some of your results will be articles that you won't be able to access. We can, however, get most articles for you from another library if you follow this link and fill out the request form.