How can I put a task from the archive back on the board?

Archived tasks are accessible with the folder icon, shown at the top of all columns, that have an archive enabled. The task archive folder icon

Once in the Archive, right-click the card you want to un-archive, and an option to Put back on the board will be displayed.

To select multiple cards from the archive, click them with the CTRL key pressed: How can I put a task from the archive back on the board