There's a quite a few steps to this process but essentially you will need to connect your on premises network to your Azure VNET using either a site-to-site VPN or ExpressRoute connection. Then you can build a domain controller VM in Azure and have it join your existing on premises domain.
Here's an overview article for getting started: https://learn.microsoft.com/en-us/azure/architecture/reference-architectures/identity/adds-extend-domain