1. Go to Lists > Manage Lists.
  2. Click the Manage Basic and Advanced Lists block under List Actions.
  3. Click on List Admin.
  4. Click on the gray arrow next to Access.
  5. Select Advanced User Access.
  6. Search for the user by last name and click on the ">>" next to their name.
  7. Click Save & Exit

You can also give all users with a particular Role Advanced List access by selecting Advanced Role Access instead