If you have been given privileges to delete assets in an archive, you can select the files and open the Asset Information panel (keyboard shortcut T) where you find the Delete icon that looks like a trash can on the Information tab. Click it to delete the selected asset(s). You need to click it twice to confirm the delete operation.
Depending on how the FotoWeb server has been configured the files are either deleted immediately or simply moved to an isolated area where they await permanent purging.
Tip: You can also delete selected assets by pressing Delete on your keyboard!