To share a list, you need to be authorised in the app.
Open the list you would like to share and tap the sharing icon in the upper right corner to invite your contacts to share the list. Tap the round button with a plus in it to proceed to your contacts.
If you have already shared your lists with others before, the app will display these people among your recent contacts. Tap on the desired contact to add it to your list. You can also untap the person to stop sharing a list with him/her:
If you do not have the required person the contacts list, enter his/her email in the contacts entry field and tap the square button with plus in it:
Person you've shared the list with will see the shared list among his/her lists. Those who don't have an account in the application yet will get an email with the invitation to the shared list.