Having obtained one of the Elder Scrolls, return it to Paarthurnax atop the Throat of the World so that you can use it to gaze into the past and find out how the ancient Nords used the Dragonrend shout to defeat Alduin.
When you arrive back at the mountaintop, Paarthurnax will tell you he sees something different in you, that you must have the Elder scroll now. He’ll then tell you to go to the time warp and read The Elder Scroll.
Upon viewing the Elder Scroll while standing in the time warp, you will see a vision of the past, and the prior heroes who defeated Alduin standing ready for the coming battle. When Alduin attacks, they will use the Dragonrend shout, and from watching them do so you will have learned it. Watch the rest of the battle.
After the ancient battle is over and your glimpse into the past ceases, the Alduin of the present will appear at the Throat of the World. Paarthurnax and Alduin will take flight and battle in the air. When the moment of opportunity is at hand, use the Dragonrend shout on Alduin, forcing him to the ground.
Alduin will take off again as soon as he recovers from the effect of the shout, but you want him on the ground as much as possible, so you should try to continue using the Dragonrend shout immediately after it recharges each time, as this will prevent Alduin from taking off again and keep him grounded for the whole fight.
This will be a hard battle; Alduin has a huge pool of health and does a lot of damage. Keep pummeling him with your preferred means of attack and eventually he’ll be unable to continue the fight, and will tell you that he underestimated you, but that no one can defeat him, not even Dovahkiin. He will then depart.