Oh, and since you may have been asking about how to cut out a “range”: put the playhead at one end of the range, the mouse at the other and press Ctrl-x. You can also use a selected marker as one of the boundaries. See the previously referred to document.
click on the track you want to edit, and while holding your mouse at the right place. press “s” The track will be split at that point. As pleasebeus said you can then drag the edges if the cut was not quite at the right place. Click to select, and press “del” to remove pieces.
In ardour we don’t go in for a multitude of different tools. The default tool (“object mode”) will let you split the selected region(s) at the current edit point (by default, wherever the mouse is) by pressing “s”. You can also click with button1 or button2 in the colored bar the bottom of the region to trim from the start or to the end. You can also drag the ends of the colored bar to resize the region after it has been trimmed.
This and more is explained (with some now-unnecessary historical context) here and also in the manual.
Note: we are generally moving away from “range mode” editing (buttonpress/drag/release), although it still exists at this time.
You can cover a range and delete, yes. Or you can split by creating a new region (right click on the range and choose “create region in place”).
The reason the process is a bit different is that Ardour is non-destructive so the original will always be there for you - you can drag the end of your new regions to see the bits you deleted.