I recently created a script to create a VM from an existing disk in Azure, using the v2 or ARM model.

This script created a new network but in most instances a network will already exist and although you will create a new NIC you will want to place this VM into an existing subnet.

The extract below can be used to create a new NIC but add this to a named vNet and Subnet.
When you define the VM configuration you would use this to be the NIC.
Finally make sure this (if the first NIC) is set as -Primary

#Networking
$NicName = $vmName + "NIC-Prod"
$Vnet = Get-AzureRmVirtualNetwork -Name "hubsydvnet" -ResourceGroupName $RGName
$SubnetProduction = Get-AzureRmVirtualNetworkSubnetConfig -Name "Sub-1" -VirtualNetwork $Vnet
$Nic = New-AzureRmNetworkInterface -ResourceGroupName $RGName -Name $NicName -Subnet $SubnetProduction -Location $Location

#Define VM Configuration
$VMConfig = New-AzureRmVMConfig -VMName $vmName -VMSize "Standard_DS2_v2" |
Set-AzureRmVMOperatingSystem -Windows -ComputerName $vmName -Credential $Cred -ProvisionVMAgent -EnableAutoUpdate |
Set-AzureRmVMOSDisk -Name $OSDiskName -VhdUri $OSDiskUri -CreateOption FromImage -SourceImageUri $URIofuploadedImage -Windows |
Add-AzureRmVMNetworkInterface -Id $Nic.ID -Primary

Disclaimer:  Please note although I work for Microsoft the information provided here does not represent an official Microsoft position and is provided as is.