By vibrating particles through a medium.
Take sound waves for example (or any other mechanical waves):
Sound travels through a medium by vibrating the particles in the medium. The particles simply move back and forth. Never actually going anywhere.
The back and forth movement is the disturbance in the medium.
Waves in classical physics have zero momentum. What does the disturbing is as mentioned, just vibrations. This shows that energy is transferred as the vibration spreads throughout the medium.
In quantum mechanics, you will see that particles can act as waves thus having momentum in their wave-particle duality.