Installing Drupal 8 in the traditional way is documented both on Drupal.org and in the INSTALL.txt file found inside the /core folder of the installation, so I won't go into it here. I will, however, mention that a better way of installing Drupal 8, especially for developers, is by using the accepted Composer template for Drupal 8 projects found on GitHub (https://github.com/drupal-composer/drupal-project). However, the instructions for setting up your site are well covered there as well.
Instead, let's talk a bit about the technologies that power (or are needed by) Drupal 8.