I assume some have already configured domain controller on-premise. It is almost the same, when you do it in Azure, accept for few things. But those are important things.
1. Set a static IP for your domain controller
Actually your IP address stay persistent for 45 years if you do not stop your VM. But if you do stop\deallocate your VM - you might get another IP address after start. And that is (softly said) not so good for domain controller and DNS server.
So make sure to confiure a "static" IP for your DC, like this, using powershell:
(If my vm name is myTestDC and corresponding cloud service name is myTestDC)
$dcvm = Get-AzureVM -ServiceName myTestDC -Name myTestDC
Set-AzureStaticVNetIP -VM $dcvm -IPAddress 192.168.0.4 | Update-AzureVM
2. Configure location of NTDS and SYSVOL to be on Data disk, not OS disk
provides us with 2 types of disks - OS and Data. Where as OS disks are
using caching by default, and Data - not. So make sure to attach an
extra Data disk to your DC and configure your ntds and sysvoll to be
3. Modify you network DNS to include new DNS server
x. And another, rather tiny but important thing :) Administrator username is not allowed to use in Azure, so - say my administrator name is superAdmin, password superPassword, and I created domain superDomain.Test with netbios name superTest. Logging into my DC after restart is superTest\superAdmin with password superPassword.
PS: Howether, if you demote your DC - suddenly you will need to login with .\administrator and password superPassword. ...Assume it is a bug, not a feture.