Not much documentation on PowerShell loops.

Documentation on loops in PowerShell is plentiful, and you might want to check out the following help topics: about_For, about_ForEach, about_Do, about_While.

foreach($line in Get-Content .\file.txt) {
    if($line -match $regex){
        # Work here
    }
}

Another idiomatic PowerShell solution to your problem is to pipe the lines of the text file to the ForEach-Object cmdlet:

Get-Content .\file.txt | ForEach-Object {
    if($_ -match $regex){
        # Work here
    }
}

Instead of regex matching inside the loop, you could pipe the lines through Where-Object to filter just those you're interested in:

Get-Content .\file.txt | Where-Object {$_ -match $regex} | ForEach-Object {
    # Work here
}