Ardour is designed to work best with a three button mouse equipped with a scroll wheel. While it can be used with a two button mouse or touchpad, at least two key operations will not be (easily) available:
It is strongly encouraged to invest in a three-button mouse. A good quality mouse (especially one with a weighted, latchable scroll wheel) will make the use of Ardour vastly more efficient. They are cheap, and time is not.
For information on how to use the mouse in Ardour, see Using the mouse.