Lets say you have a SharePoint group named "Notify Members". They would like to receive an alert when a document is added to the document library "Business document". Here are list of PowerShell Commands to achieve the functionality.
$web = Get-SPWeb "http://localhost/mysite/"
$group = $web.Groups["Notify Members"]
$list = $web.Lists[" Business document"]
foreach ($user in $group.Users){
$alert = $user.Alerts.Add()
$alert.Title = "Alerts"
$alert.AlertType = [Microsoft.SharePoint.SPAlertType]::List
$alert.List = $list
$alert.DeliveryChannels = [Microsoft.SharePoint.SPAlertDeliveryChannels]::Email
$alert.EventType = [Microsoft.SharePoint.SPEventType]::Add
$alert.AlertFrequency = [Microsoft.SharePoint.SPAlertFrequency]::Immediate
$alert.Update()
}
$web.Dispose()