A quick todo list for setting up a freshly cloned project.
Install the dependencies with Composer.
# cd in your project directory composer install composer dumpautoload -o
Check if the values in config/app.php meets your needs, depending where (staging, dev, ...) and how (php -S, artisan, vm with a domain, ...) you are running it.
If you have to go for a Drupal core update from a previous install based on composer_manager or drush (both deprecated), consider installing something robust, Composer friendly, that excludes vendor and core for a lightweight repository and enables CI and automation tools like Phing, Behat, PHPUnit, CodeSniffer, ...
If you don't have Drupal VM installed, head to the documentation.