How to include a new file in theme

Lets take a look in the twentysixteen theme.

Line 18/19 (inside the loop) of single.php shows actualy all you need/want to know, it uses:
get_template_part( $slug, $name );

• // Include the single post content template
• get_template_part( 'template-parts/content', 'single' );

That means actualy for WP:

• Get a (partial) template for a (in this case) single post.
• Look in the folder (from within your theme directory)
  template-parts for a file which has the name
  content-single.php.
• ‘Grab’ what is in it (lets say <?php echo 'Hello World'; ?>) and display – Hello World – as content for that post.

This way it already has the header and footer as you want it/as (imho) should be done.
There are other ways to load -templates- (through a function) but that was not the question here.

Note: You can do this also with page.php / taxonomy.php / archive.php / category.php etc.

See the codex for: Theme development
See the codex for: Linking to Core Theme Files

I hope this explains (although in a digest size) the basics of how you can use get_template_part.