EndNote Desktop: Sync Then Share
Share your entire EndNote Desktop library or just a single group of references with another EndNote user.
First create an EndNote Online account, sync your Desktop EndNote library with your online account, then share part or all of your library.
Short silent videos 2-9 of this playlist demonstrate the process for Windows.
EndNote Basic: Share Groups Only
In EndNote Basic you must file your references into groups and then you can share those specific groups with others.