Powershell with WinForms - returning user input into a text box from a function

In your formTextBox function, you're trying to return the text of a text-box control before the dialog has even been displayed, so that won't work.

Instead, return the control from the function, whose .Text property you can examine after the dialog has been closed:

function formTextBox($tboxLocW,$tboxLocH,$tboxSizeW,$tboxSizeH) {
    $textBox = New-Object System.Windows.Forms.TextBox
    $textBox.Location = New-Object System.Drawing.Point($tboxLocW,$tboxLocH) 
    $textBox.Size = New-Object System.Drawing.Size($tboxSizeW,$tboxSizeH) 
    $form.Controls.Add($textBox)
    return $textBox # Return the text box itself (the object)
}

# ...

# Create the text box, add it to the form, and store it in variable $a.
$a = formTextBox -tboxLocW 10 -tboxLocH 50 -tboxSizeW 260 -tboxSizeH 30

# ...

# Invoke the dialog and act on how it was closed.
if ($form.ShowDialog() -eq [System.Windows.Forms.DialogResult]::OK) {
    $textA = $a.Text  # Get the text box' text now.
    Write-Verbose -Verbose "OK clicked: text box `$a contains: $textA"
} else {
    Write-Verbose -Verbose "Dialog was closed without clicking OK."
}

Furthermore, it looks like you were trying to react to the event of the OK button getting clicked with the following code, which also won't work, because again, it executes synchronously, before the dialog is ever shown:

if($okbutton.Clicked){  # DOESN'T WORK - event delegate needed instead
    Write-Host $a    
}

Instead, you need to set up an event handler (event delegate), which in PowerShell takes the form of <control>.add_<event-name>({ ... }); in the case at hand, we want to react to the Click event:

$OKButton.add_Click({
    param([object] $sender, [System.EventArgs] $evtArgs)
    Write-Verbose -Verbose "Button '$($sender.Text)' clicked."
})

The script block ({ ... }) will now be invoked when the button is pressed, whenever that occurs. The param() block declares the two arguments that are passed to your event delegate, although you can omit the declaration altogether if you don't need information about who originated the event ($sender) or the specifics of the event ($evtArgs), if any.

Note: To determine a given [System.Windows.Forms.Control] type's available events as well as the specific [System.EventArgs] subclass that is passed, you can use something like
New-Object System.Windows.Forms.Button | Get-Member -MemberType Event