Open your skins/yourskin/_main.php file and look through it a bit. Eventually you'll find something that looks like "$Item->views()", or at least very similar to that. Whatever the line actually is, you'll need to wrap it in a login check, like this:

if( is_logged_in() ) {
* the line that displays the view count
}

Be a bit careful with your php stuff too. Use a "smart" editor like html-kit (and there are many others) so that you get color-coded syntax. It will help you see if your php tags are open or not. For example let me grab a quick piece of code with php open and closed and open again...

<div class="bSmallHead">
	<?php 
	locale_flag( $Item->locale, 'h10px' );
	echo ' &nbsp;';
	$Item->issue_date('F jS, Y');
	echo ' by ';
	?>
	<a href="<?php echo url_add_param( $Blog->get( 'blogurl', 'htmlattr' ), 'author='. $Item->get('creator_user_ID') ) ?>" title="<?php echo T_('Browse all posts by') ?> <?php $Item->author() ?>"><?php $Item->author() ?></a>
	<?php 
	echo ' (';
	$Item->msgform_link( $Blog->get('msgformurl') );
	echo ')';
	?>
	</div>

<div class="bText">
	<?php 
	$Item->content();
	link_pages();
	?>
	</div>

The "<php" line starts php stuff, and "?>" ends it, so anyway it shouldn't be that hard after you get a handle on which parts are php and which parts are html.