In TextPad:
With the mouse, Left-Click + Alt + Drag. Note that if you first use Alt, and then Click-and-drag, it does not work (at least for me). Ctrl+Alt instead of Alt also Works.
For pure keyboard, no mouse, enable Block Select Mode with Ctrl+Q, B. Or use the sequence Alt, C, B, to do it via the Configure menu.
Warning 1: if Word Wrap is enabled, then Block Select Mode will not be available (which is somewhat logical). First disable Word Wrap. This was causing me some trouble, and this gave me the answer.
Warning 2: if you mean to insert text in every selected row by typing, you have to use Edit, Fill Block. Other editors let you type in directly.