Sharing a list will upload a copy to the server and provide you with a share code.
Give this to the person you wish to share a list with and you will be able to share changes to the list with each other.
Your temporary share code is:
Give this to the person you wish to share with. On their device they click on the "Join" button on the main screen and enter the code to join.
List Joining
Enter a share code from list owner to join and share changes to a list. The other person can find the share code by going to the list they want to share and hitting the "Share" button.