9.1 Check out a new project
composer install
it will read the composer.json file which lists all the dependancies and patches and scripts and it will then download everything and run everything...
9.2 Grab the latest updates from other developers
composer install
9.3 Grab the latest versions of project dependancies
composer update drupal/admin_toolbar
N.B. if you run composer update without specifying a project it will update all the projects dependancies, so be careful...