Here is simple example of how to retrieve local NT account (user or group) SID with powershell:

PS E:\TEST> $objUser = New-Object System.Security.Principal.NTAccount("alesk")
PS E:\TEST> $strSID = $objUser.Translate([System.Security.Principal.SecurityIdentifier])
PS E:\TEST> $strSID.Value
S-1-5-21-1384281309-654973799-88281384-1000

To retrieve SID of domain user:

PS E:\TEST> $objUser = New-Object System.Security.Principal.NTAccount("acmedomain\alesk")
or
PS E:\TEST> $objUser = New-Object System.Security.Principal.NTAccount("acmedomain","alesk")

PS E:\TEST> $strSID = $objUser.Translate([System.Security.Principal.SecurityIdentifier])
PS E:\TEST> $strSID.Value
S-1-5-21-2377153150-1065022559-2428809875-3485

I found this tip among tips published on MS Technet Windows PowerShell tips.