Processing Queues

I have several different lists (members, board, newsletter). Some are marked private and others are marked public

When creating and sending a campaign to two or more lists at the same time, the campaign is not sent out.

What I have to do is send to one list, then go to List Campaigns and select the one just sent, mark it as a Draft, and then select the other list(s) and process it.

How do I setup phpList to send to multiple lists whether they are public and/or private?

What do you mean by this? Look on the event log page to see what phplist did with the campaign. If you enable VERBOSE in the config.php file then there will be more information.