In most databases there will be a link that either says "pdf full text" or "link to full text". Those will provide the quickest access to articles. If those are not there, there should be a yellow "Get it @ ASU" link that will check to see if we have access to that article.
There are other ways to see if we have a certain article. You could use these options if the database links haven't found the item and you want to do a final check. But it is much more likely that you would use one of these methods to find an article when you have gotten a reference from another source, such as a bibliography, and already know the citation information (journal name, volume number, date, etc.).
Search the title of the article in Google Scholar. If you put the title of the article in quotation marks into the search box it will be a little more specific, but that's not always necessary. Usually just a simple cut and paste will work. Click on the title of the article or use the "get it @ ASU" links within Google Scholar to take you to the article.