You want a WordPress network aka WP multi site. There is complete documentation on WP Codex. https://codex.wordpress.org/Create_A_Network
In Step 3: Installing a Network, select the sub domain option when prompted. If you are converting an existing site, you will get locked into sub folders instead of sub domains. Go with a clean install to avoid this.
New sites are created as sub domains and no plugin is required to manage domain names.
Each site has its own content, theme, widget options. Users are assigned rights individually for each site or designate a super-admin with access to all.
Network administration (super admin) is able to allow themes and plugins across your full network or site-by-site if you wish.
For more information, or a guide to the documentation on the Codex, the folks at WPMU have a great new write-up on WordPress networks: https://premium.wpmudev.org/blog/ultimate-guide-multisite/