This would be really simple in your theme, e.g. node-foo.tpl.php for the content-type foo, that has a field "video"
<?php if(!empty($field_video[0]['view'])): ?>
<div class="block video">
<?php print $field_video[0]['view'] ?>
</div>
<?php print $field_some_other[0]['view'] ?>
<?php print $field_the_other_one[0]['view'] ?>
<?php endif; ?>
Some notes on style and best practices:
I prefer the if/endif in templates, others prefer the if() {}. Technically little difference, I think elseif; is more readable in HTML.
Technically it is not correct to simply print a value, but one should use drupal_render(). I personally still prefer print, because of its transparancy and simplicity. Drupal_render(), however, registers what it has "rendered" and allows you to drupal_render($node) at the end, to render all unrendered fields; very usefull if you decide to add fields later on, whithout having to change the entire template every time you do so. Drupal_render is not available in the tpl.php, but in the preprocessing: as sayd, a lot less transparent and slightly more complex.
Dont! Ever! print the $field_foo[0]['value'], always the ['view'] part: the first is unescaped and may (will!) contain XSS injections and the likes.
The strange nested array ($field_foo[0]['value']) is a result of the multiple-fields option in Drupal. A better way would be to always iterate over each field and never just render, hardcoded, the first ([0]) item. However, for reasons of readability, simplicity and transparancy, I prefer to hardcode the indexes in my template. Others (rightfully) disagree with me on this.