They log into the panel with their email address (the one you used when you granted them access to the relevant domain) and their password. Essentially, this email address serves the function of the "WebID". I agree, it is not very clear, and the old WebID usage is still scattered about the documnentation in various places.
That said, you will find that if they login to the Web Panel with the email address and password which you granted access to a given domain to, they can simply go to Mail -> Announce List/Discussion Lists and create list for the domain for which they have been granted access.
Further down the page where you granted them (by email address) access to the relevant domain, you could have also granted them access to some, or all, or the administrative functions of your account (including existing and future mailing lists - it looks like there is a typo in the panel text, as "future" is omitted there) at the time when when granted them access to the domain.
If you did not do that at that time, you can add additional privileges from the COntrol Panel -> Users -> Account Privileges screen by selecting the "Edit privileges for " link you will find immediately below the list of presently granted privileges for that user.
You will then be presented with a screen that allows you to grant them other administration privileges, including the ability to "post" to existing mailing list(s).