What needs to be done/added on Apple MacBook Air in order to join domain and be managed?

You can bind the Mac to your Active Directory fairly easily. In the Users & Groups control panel, you have a menu for Login Options. You can Join... a Network Account Server from this window.

Once bound to the domain, you can use additional features found in the Directory Utility. The main thing I do for laptops is Create a Mobile Account at Login. This is like an offline profile that allows the user to login via AD credentials even while away from the network. You can also set the AD groups that are allowed to administer the system via options in this dialog. By default, Domain Admins can manage the system. And any domain user can login by default as well (I believe). Use the DOMAIN\username syntax once you've bound to AD.