Login to MySQL as the root MySQL user and create the database that will hold the LiveJournal data:

$ mysql -uroot -p
mysql> CREATE DATABASE livejournal;
mysql> GRANT ALL PRIVILEGES ON livejournal.* TO 
     > lj@'localhost' IDENTIFIED BY 'ljpass';

If you know what you're doing, you can set this up however you like. You tell LiveJournal how to connect to its database server(s) in your ljconfig.pl, as detailed in: Section 4: Configuring %LJ::DBINFO.