How to add Login/Register link in the right header in Skeleton theme
Drupal has this feature where you can create menu links for user/login and user/logout and only the appropriate one will be displayed automatically. Same goes for user/register.

So create a new menu, add links "Login" (user/login), "Logout" (user/logout) and "Register" (user/register). In admin/structure/block move your new menu to where you need, and apply necessary styling.