I can find the VM by using
$vm = Get-AzureRmVM -ResourceGroupName "MyResource" -Name "MyVM"
But how can I find the network interface associated with this VM?
Once you have your VM in a variable $vm (as shown below)
$vm = Get-AzureRmVM -ResourceGroupName "MyResource" -Name "MyVM"
You can get the NIC by finding the interface that matches the ID from your VM
$nic = Get-AzureRmNetworkInterface
| Where {$_.Id -eq $vm.NetworkProfile.NetworkInterfaces[0].Id}