You do not need server racks. You need a computer to install Windows Server on. Once you have installed the operating system you install Active Directory onto that server. Your question requires too much explanation regarding Active Directory. You are essentially asking for the documentation regarding how to do a multi-site setup. Install it to a single server first and then build upon that knowledge by going to docs.microsoft.com and doing some research/reading. I've put some basic installation directions for you below without explaining why. It's too much verbiage.
A Windows Domain Controller runs on Windows Server. It is a feature that the server can have installed/enabled.
To view all of the possible roles you can open a Windows Administrative Powershell session and type the following command
A list of the available features will scroll by. One of them is "Active Directory Domain Services". You can initiate an install of Active Directory by using the 'Install-WindowsFeature' Powershell cmdlet.
Type the following command into your administrative powershell cli:
Install-WindowsFeature -Name AD-Domain-Services -IncludeManagementTools -Verbose
This will initiate the installation of Active Directory and make the server a domain controller. This role is central to idea of a centralized security context for all of your workstations, servers and users as well as other LDAP objects that you can act upon and manage.
Once the installation is complete you can view the available tools to manage your server's domains services by opening the administrative tools section in your start menu.
I suggest you read the manual by following this link and seeing the other methods of deploying Active Directory to a Windows Server as well as researching what Active Directory is and what it is used for.