How to connect a sql database hosted in Azure VM from from on-premise server. Please advice

As mentioned there is no difference with any other SQL Server hosted on-prem. You have to check if TCP Port 1433 is open.

You can use Powershell and DBATools and try below from your client computer

Test-DbaConnection -SqlInstance <SQL Server Name>

Regards
Javier

There is absolute no difference in the way to connect to on-premise vs VM in the cloud; why do you think so?
You just have to take care that an existing FireWall allows the access.