Aragorn (Viggo Mortensen)’s Timeline and Summary

The three adventurers are tracking the uruk-hai (who are carrying Merry and Pippin back to Isengard).
They meet Éomer who tells them they killed a company of orcs.
Upon searching the remains, Aragorn realizes the hobbits made their way into Fangorn Forest. Reluctantly, they follow.
In Fangorn they meet Gandalf who they initially try to attack, mistaking him for Saruman.
Gandalf ensures them of Merry and Pippin's safety, and they follow him to Rohan to help overthrow Saruman's control of King Théoden.
This being accomplished, they follow the people of Edoras to Helm's Deep, where Théoden hopes to defend against Saruman's army.
They defend against the warg riders who attack the Rohirrim as they travel towards the fortress. The battle is won but many are lost, including Aragorn who falls off a cliff into a river.
Aragorn is found by a horse and carried back toward Rohan, where Legolas and Gimli are helping make preparations for the defense.
Aragorn joins in the preparations and greets the Rivendell elves when they arrive.
Together, they defend against the invading orc army, performing many heroic feats in combat.
But, despite their best efforts, the outer wall falls and Helm's Deep is all but lost.
Aragorn inspires Théoden to ride out one last time. Gimli and Legolas aren't far behind.
As they ride they see Gandalf and Éomer upon the hill; the day is won.