gistfile1.php

$args = array(
    ...

    'meta_query' => array(
        'relation' => 'AND',
        array(
            'key' => 'publish_date', // name of your custom field
            'value' => time(),            
            'compare' => '<',            
        ),
        array(
            'key' => 'expire_date', // name of your custom field
            'value' => time(),            
            'compare' => '>',            
        ),
    )
 );