Open the windows called "Mail & Newsgroups".
The account wizard will pop up if you have no account configured yet. Otherwise start the wizard through the menu:
Edit → Mail & Newsgroups Account Settings...
New Account Setup
Activate "Newsgroup account", then click "Next".
news.albasani.net is the usual setting. See SSL and alternative ports for other possibilities.
The account name can be chosen freely, the server name is only a suggestion.
The line "Outgoing User Name" has no meaning. SeaMonkey builds that value out of the email address. It is never used, though.
Subscribe News Groups
In the folder lists you should now have an entry for the news server. Select it, then chose menu item File → Subscribe...
Fill in the value of "Username:" from the email reply of your account registration.
Click on "Refresh".
SeaMonkey will now open a connection to server, authenticate, and download the list of available newsgroups.