I'm configuring zp-config.php.example and I don't understand how $conf['mysql_database'] = ""; works. I created a database called zpimages. Do I put any tables in it? Also, what do I use Database table Prefix for?

Don't mess with zp-config. Let Setup do the edits. Just tell it your Database information and it will do the rest.

Actually I was referring to zp-config.php.EXAMPLE where you have to make to make changes. It's this section

////////////////////////////////////////////////////////////////////////////////
// Database Information (the most important part!)
////////////////////////////////////////////////////////////////////////////////

$conf['mysql_user'] = "";
$conf['mysql_pass'] = "";
$conf['mysql_host'] = "localhost"; // Won't need to change this 90% of the time.
$conf['mysql_database'] = "";

The instructions you found while browsing the source may be out of date. Just follow the instructions on the website and run the automated setup. You should be good to go assuming your file permissions are set correctly.

You state you created a database named "zpimages". Depending on how you set your database up, you should tell setup your database name is "zpimages", or "[USERNAME]zpimages". (replace "[USERNAME]" with the database username.) It will create the necessary tables for you automatically. You usually don't need to modify the table prefix unless you are installing into a shared database. I believe the default is "zp".

If you are installing into a shared database, for instance Wordpress, your wordpress tables would begin with "wp" and your zenphoto tables would begin with "zp". This prevents tables by the same name from being overwritten in the same database.