How to theme a specified node?
Yes, you can use templates for this; there's an explanation of how it works on Drupal.org.

To override the page template for a specific node you would use a template file with a name like:

page--node--1.tpl.php


Where 1 is the nid of your node.

The name of the file is based on the path of the page you want to provide the template for, essentially with / characters changed to --. So for the path '/node/1/edit' the template file would be named:

page--node--1--edit.tpl.php


The easiest way to start the new template file is just to copy the existing page.tpl.php source into your new file, and add/edit what you need.

If it's the node specifically you want to theme (and not the whole page), you can provide template files for it in much the same way. There are more examples in the link above, but basically for node/1 the file would be:

node--1.tpl.php


Remember to flush the caches when you add the new template file so the changes get picked up.