The Backup-SqlDatabase cmdlet that comes with the SQLPS modules allows you to perform database backups using different options. When you run Get-Help Backup-SqlDatabase, you should get a full list of syntax and examples. The options you get with this cmdlet are similar to the options you have with the BACKUP DATABASE T-SQL command. The following is an example script that performs a full database backup on a timestamped backup file:

Import-Module SQLPS -DisableNameChecking

#current server name
$servername = "ROGUE"

#$server = New-Object "Microsoft.SqlServer.Management.Smo.Server" $servername

$dbname = "Chinook"
$currdate = Get-Date -Format yyyyMMddHHmmss
$backupfolder = "C:\BACKUP\"

#generate backup file path and...