Login and click on your user name to expand the menu on the top right.
Click on "My Account"
Select "Invite Team"
Enter an email for the new user
Select the appropriate access level for the new user. See here for info about different user types.
Send invite to the new user email address. The new user will be in "Pending Invites" tab until they access the verification email in their email inbox.
To set access to a specific calendar or publisher site:
View new users now in "Pending Invites"
Select "Edit" to set specific sites the new user will be able to access.
When an invite is sent, the user will receive an email with a verification link. If you have already set their calendar access in steps 7 & 8 then nothing more needs to be done for them to get started.