You must have heard or read of using Start-Transcript and Stop Transcript to capture your entire PowerShell session. But if you want to capture only the output and error generated by a script, execute your scripts in below format.
PS> powershell.exe –noprofile –file c:\temp\Script.ps1 > C:\Temp\Log.txt
C:\Temp\Log.txt stores output of your script and the errors generated. This is useful when executing scripts for multiple computers.