To invite a member to have access to your Action List you can use the form on the "List Settings" page. Check the "Send Email" option to send an email notification.
If you invite a member who does not already have an Action-Check account, they wil be send an email inviting them to register. They simply need to register for an account on Action-Check and they'll be able to see the Action List you have invited them to be a member of.
Users who already have an Action-Check account will be notified that they have access to a new list and when they connect to their account they'll be able to see the new list.
Once a new member have been invited, you can assign a role for that user.
By default the "Staff" role is assigned. If you have a Pro account you'll be able to alter this to best match the members requirements. See: List Settings