To share your desktop EndNote library, you must first syncronize (sync) it with your Endnote online library. If you've already done this, then just go to File > Share and enter the email addresses of the people you want to collaborate with. If you haven’t, start by clicking the Sync icon on the toolbar. You will be prompted to enter your account credentials or create a new account, if you haven’t done so already. Once your account is created and your library is fully synced, you can begin sharing.
Sync times can vary depending on the size of your library. Be sure to check the Sync Status, located in the My Library panel, to make sure your library is fully synced before sharing.