One of the superb things about WordPress is that it will automatically convert YouTube URLs into embeds (as well as URLs pointing to Vimeo, Flickr, Hulu etc.)
For example, the video you see embedded on this post was supplied from within the WordPress post editor like this:
How to change the size for an individual embed:
If you need to make an embed bigger or smaller for a particular page or post, you can override the global media settings by adding a little code to your post, like this:
How to set the size of automatic embeds for your entire WordPress site in WP 3.5 and above:
Add this code to your theme’s functions.php document, setting your own width and height of course.
add_filter( 'embed_defaults', 'bigger_embed_size' );
return array( 'width' => 600, 'height' => 430 );
How to set the size of automatic embeds for your entire WordPress site in versions before 3.5:
Login as the WordPress admin and go to Settings: Media. There you’ll see boxes for setting your maximum embed height and width. This will change the width of your embeds throughout your whole site. It’s retroactive so if you change theses settings, they’ll impact embeds even on posts and pages you authored before making the update.