Alduin will use a shout to resurrect this dragon. It turns out Delphine is right and here, on a dragon burial mound, Alduin can be seen flying above. Here is where Delphine has predicted that the next Dragon will be resurrected.
The Last Dragonborn and Delphine both travel to Kynesgrove during this quest. Once the keep is escaped through the cave, he will be seen flying above, and will fly away to the east. During the Dragonborn's escape from the village and into Helgen Keep, he will be seen fighting a number of Imperial soldiers, and may land and attack the Dragonborn in front of the keep if the Dragonborn does not escape quickly enough.
Once the Last Dragonborn is placed on the chopping block, he will land on top of the tower above and use the roar that summons a storm raining meteors down from the sky to cause havoc and destruction in the settlement.
During the executions, Alduin will be flying above Helgen, and his roars can be faintly heard.