PowerShell supports multiple methods for starting a process with the most common being the Start-Process cmdlet. Others include the Call Operator (&) or using Dot Sourcing. First lets take a look at the Start-Process cmdlet.
Start-Process
Start-Process "C:\Mozilla Firefox\firefox.exe" -ArgumentList "www.msdn.com"
#
# Open an admin session of PowerShell ISE
#
Start-Process PowerShell_ISE -Verb RunAs -Wait
Call Operator (&)
#
# Start Notepad and open Text.txt
#
PS C:\Windows> & "C:\Windows\Notepad" Test.txt
#
# Create a variable with it's contents being a command
#
PS C:\Windows> $cmd = "Get-Process -Name *svchost*"
# Invoke the command
PS C:\Windows> & $cmd
Id ProcessName
-- -----------
3260 SMSvcHost
3336 SMSvcHost
564 svchost
776 svchost
Dot Sourcing
# Open Paint
. "C:\Windows\System32\mspaint.exe"
# Call a PowerShell script that adds functions
. "C:\Scripts\CommonFunctions.ps1"
If you are interested in starting a process on a remote machine
take a look at PsExec