Ok so hope this helps someone. Unless you want to query the database directly, the trick is to include the following:
$event = Ai1ec_Events_Helper::get_event($post->ID);
thereafter you can retrieve the variables, for example:
<?php query_posts('post_type=ai1ec_event');?>
<?php while ( have_posts() ) : the_post(); ?>
<?php $event = Ai1ec_Events_Helper::get_event($post->ID); ?>
<?php echo '<h5><a href="'.get_permalink().'">'.get_the_title().'</a></h5>'; ?>
<?php if( $event->multiday ) echo 'ai1ec-multiday' ?> <?php if( $event->allday ) echo 'ai1ec-allday' ?>
<?php echo esc_html( $event->start_time ) ?>
<?php echo $event->timespan_html ?>
<?php echo $event->venue; ?>
<?php if( $recurrence ): ?>
<?php echo $recurrence ?>
<?php endif ?>
<?php if( $event->cost ): ?>
<?php echo esc_html( $event->cost ) ?>
<?php endif ?>
<?php if( $contact ): ?>
<?php echo $contact ?>
<?php endif ?>
<?php if( $categories ): ?>
<?php echo $categories ?>
<?php endif ?>
<?php if( $tags ): ?>
<?php echo $tags ?>
<?php endif ?>
<?php endwhile; ?><!-- End the Loop -->