The size of the player you can set in sidebarclip.php:
'width'=>300,
'height'=>250 ));
to another value
use style.css to arrange that players as you like - first you have to get them to show up..

The post actually is filtered for an oembed video, only this video will be displayed in a size you can set.

For testing I just do it on a theme demo site here:
http://themes.go41.de/?wptheme=arthemix_dev

First of all you should have a post with an embeded video, WordPress allows you to embed a video by just inserting the URL in a single line in the post editor, like this:

http://www.youtube.com/watch?v=wLph9-ZkMX8

looking at the single post it should show you the video.

Let's do it (sample should be to see here http://themes.go41.de/?wptheme=arthemix_dev )

STOP: BACKUP YOUR FILES WE ARE GOING TO CHANGE, just in case...

We have to edit sidebar.php and add two lines to load another template called sidebarclip.php (we will create this file later)

Lines to add in sidebar.php: (in Arthemia under div id="sidebar" just above div id="sidebar-ads" )

<?php if(file_exists(TEMPLATEPATH . '/sidebarclip.php')) { // get the clip-script
	include (TEMPLATEPATH . '/sidebarclip.php'); } ?>

This code just looks for the following template file in your themes folder, It's just a 'manual widget' ;-)

Create a new file called sidebarclip.php with the following content

<div id="sidebar-video">
<?php $category_id = get_cat_ID( 'Videos' ); // set your category name here, if you know the ID use $category_id = 6;  ?>
<h3>Featured Video <a style="float: right;" href="<?php $category_link = get_category_link( $category_id ); echo $category_link; ?>" title="more Videos">more Videos</a></h3>
<?php
query_posts('posts_per_page=1&cat=$category_id');
if ( have_posts() ) : while ( have_posts() ) : the_post();?>
<?php if((function_exists('resizeMarkup')) && (function_exists('get_embedhtml'))) {
	$resizedvideo = resizeMarkup((get_embedhtml($postID)), array(
	'width'=>300,
	'height'=>250 ));
	if($resizedvideo != '')
			{
			echo $resizedvideo;
			} else { // if no Video
			echo 'no Clip available';
			}
		} ?>
<p>Read the post:<br /><a href="<?php the_permalink() ?>" title="<?php the_title(); ?>"><?php the_title(); ?></a></p>

<?php
endwhile;endif;
wp_reset_query();
?>
</div>

beeing here I can see something new in the sidebar already, but where is the video clip?
We still have to add some functions in functions.php of your theme folder, here the script: you should add it at the end of functions.php before the closing '?>'

// the function to resize oembed videos
function resizeMarkup($markup, $dimensions)
{
$w = $dimensions['width'];
$h = $dimensions['height'];

$patterns = array();
$replacements = array();
if( !empty($w) )
{
$patterns[] = '/width="([0-9]+)"/';
$patterns[] = '/width:([0-9]+)/';

$replacements[] = 'width="'.$w.'"';
$replacements[] = 'width:'.$w;
}

if( !empty($h) )
{
$patterns[] = '/height="([0-9]+)"/';
$patterns[] = '/height:([0-9]+)/';

$replacements[] = 'height="'.$h.'"';
$replacements[] = 'height:'.$h;
}

$patterns[] = '/<\/param><embed/';
$patterns[] = '/allowscriptaccess="always"/';

$replacements[] = '</param><param name="wmode" value="transparent"></param><embed';
$replacements[] = 'wmode="transparent" allowscriptaccess="always"';

return preg_replace($patterns, $replacements, $markup);
}

// get_embedhtml
function get_embedhtml($postID)
{
  $custom_field_keys = get_post_custom_keys();
  foreach ( $custom_field_keys as $key => $value ) {
    $valuet = trim(substr($value, 1, 4));
	if ( 'oemb' == $valuet ) { // look if a oembed key exists
    $oembkey = $value; //now set the the key we found as oembkey
	$oembvalue = get_post_custom_values($oembkey); //get the value of oembkey as oembvalue
	if (isset($oembvalue[0])) {
		$embedhtml = ($oembvalue[0]);
return $embedhtml;
		}
	}
  }

}

function add_transparent($oembvideo) {
$patterns = array();
$replacements = array();
$patterns[] = '/<\/param><embed/';
$patterns[] = '/allowscriptaccess="always"/';

$replacements[] = '</param><param name="wmode" value="transparent"></param><embed';
$replacements[] = 'wmode="transparent" allowscriptaccess="always"';

return preg_replace($patterns, $replacements, $oembvideo);

	return $oembvideo;
}
add_filter('embed_oembed_html', 'add_transparent');

Works! Lucky we are, but still could apply some styling to the new div id="sidebar-video" to make it look nice.

This is done in style.css, I use:

#sidebar-video {
width:300px;
float:right;
border:1px solid #DDDDDD;
background:#FFFFFF;
padding:10px 9px;
margin: 0 0 10px;
}

Try it, having problems ask for help!
Demo here: http://themes.go41.de/?wptheme=arthemix_dev in the sidebar

To change and resize the width and height of the video we are going to display, we can add a function to the theme's function.php to do this for us.
I got this function from Vinod Kumar explained here:
Dynamically Change Width and Height in embed code

So put this function into your functions.php first:

// the function to resize oembed videos
function resizeMarkup($markup, $dimensions)
{
$w = $dimensions['width'];
$h = $dimensions['height'];

$patterns = array();
$replacements = array();
if( !empty($w) )
{
$patterns[] = '/width="([0-9]+)"/';
$patterns[] = '/width:([0-9]+)/';

$replacements[] = 'width="'.$w.'"';
$replacements[] = 'width:'.$w;
}

if( !empty($h) )
{
$patterns[] = '/height="([0-9]+)"/';
$patterns[] = '/height:([0-9]+)/';

$replacements[] = 'height="'.$h.'"';
$replacements[] = 'height:'.$h;
}

return preg_replace($patterns, $replacements, $markup);
}

Having this code activated by putting it in functions.php, we can use it as explained in Vinod's post (link above).

We want to use this function to change width and height attributes throughout the oembed code we retrieved before from the WordPress database.
As explained here: http://forum.go41.de/topic/get-the-oembed-code-of-a-video-in-a-wp-29-post-from-postmeta we have already a variable assigned to the oembed code, now we just pass this variable to the function 'resizeMarkup' with new values for width and height and echo the resized video clip.
To do this we put into the loop this code:

<?php if(function_exists('resizeMarkup')) {
	$resizedvideo = resizeMarkup(($embedhtml), array(
	'width'=>300,
	'height'=>250 ));
	echo $resizedvideo; } ?>

Any questions? Sign up and ask, you are welcome.