EndNote X6 and X5 behave much the same way for Find Full Text. I have included the Preferences screens from both EndNote X6 and EndNote X5. Between these two editions of EndNote, the biggest change to the Preferences Screen is the addition of the Sync entry for connecting a Local EndNote Library with your EndNote Web Library. If you are still using EndNote X4, please refer to the EndNote X5 Preferences Screen.
Go to Edit-->Preferences-->Find Full Text
EndNote X5 Preferences Screen
While selecting references, download the pdf for an article and save it to a folder you will remember on your computer.
Search for full text AFTER importing references into EndNote using OpenURL Link.
Search for full text AFTER importing references using URL --> Open URL
Search for full text for MULTIPLE references, AFTER importing references.
NOTE: Unfortunately EndNote X4, X5, X6, or X7 does not find and attach ALL full text available using this method. Be prepared to search one-by-one using Options 1-3 above. If the articles are FREELY AVAILABLE online, they will most likely be found and attached.