When creating re-usable theme templates in Drupal 8 it's quite easy to include that template by using the following snippet.
{% include directory ~ '/templates/parts/footer.html.twig' %}
This assumes that your footer.html.twig template file is kept in the same theme as the template you are working on. It's also good practice to add the template part to a directory called 'parts' or 'components' to separate them from the normal Drupal templates.