The template should come in a folder. In that folder are a bunch of files, namely style.css, index.php, header.php, footer.php.
That folder needs to be uploaded in its entirety to your site. It goes in the wp-content/themes/ directory. You should already see a "default" and "classic" folder in wp-content/themes/. At least one of those, anyhow.
If you're going to edit the template, make sure you keep a good copy of your theme on your home computer. You can edit the themes from within the wp-admin (WordPress) Admin panel. It's in the Appearance Section, so click "Editor." Upper right corner is a dropdown menu to pick the theme you want to edit. Right column will list the sections you can edit.
The template syntax is PHP, so be careful in what you change. I expect you'll just be modifying existing text and images, but as long as you have a clean copy of the template at home, you can re-upload any files you muck up.