Leading a host of 18,000 troops from the North, Robb Stark means to confront the Lannister armies in the Riverlands and relieve the forces loyal to his grandfather which have been under attack for some time. Lord Tywin Lannister has split his forces into two armies, each numbering approximately 30,000 men. One force, under the command of Jaime Lannister, lays siege to Riverrun, the seat of House Tully. The other, under Tywin's direct command, marches north, along the west bank of the Green Fork of the River Trident, to prevent the Starks from lifting the siege, and sends scouts to reconnoiter the Stark position.
Robb and his men debate strategy, since they are outnumbered by either Lannister army. Several lords favor a direct confrontation with Tywin's forces, whilst Greatjon Umber advocates trying to outflank Tywin, get past him, and then confront Jaime's forces at Riverrun. Robb is still undecided when one of the Lannister scouts is taken prisoner. He tells Robb that he counted roughly 20,000 men in the Stark host. Robb tells him to carry a message to Tywin, telling him that "Twenty thousand Northern warriors march South to find out if he really does shit gold".
Catelyn Stark negotiates with Lord Walder Frey to allow Robb's army safe passage across the Trident at the Twins. Walder grants the passage and even contributes his levies to Robb's army, increasing Robb's numbers, in return for Robb agreeing to marry his daughter. However, after crossing the river the Stark host splits into two forces. One, of 2,000 men, moves south to confront Tywin, whilst the others move south-west to confront Jaime.
Tywin receives word that the Starks are moving against him. Believing this is the full Stark host, based on the information the captured scout returned to him, he prepares to confront it. He assigns his son, Tyrion Lannister, who has won the support of several of the hill tribes of the Vale of Arryn, to command them in the vanguard. In the event, Tyrion is disabled by an accidental blow from one of his own men and spends the battle unconscious. In his absence, the Lannisters win a crushing victory, and his hill tribesmen actually perform quite well. However, it is quickly revealed that the battle was a feint: Robb Stark only sent 2,000 men against the Lannisters, slipping the rest around the Lannister force to instead attack Jaime Lannister's forces.
Despite winning the battle on the Green Fork, the defeat of Jaime's forces at the Battle of the Whispering Wood and the subsequent joining of forces of the river lords to Robb's forces leaves Tywin's forces exposed and outflanked. He retreats his army to Harrenhal to rest and regroup.
In the books
In the A Song of Ice and Fire novels, the Battle of the Green Fork unfolds in a similar manner but with different details. As in the TV series, Robb meant to send a feinting force against Tywin whilst engaging Jaime Lannister near Riverrun. However, in the books his plan was more complex due to the different positioning. In the books, Tywin's army was located east of the Green Fork, near the ruby ford over the river. From this position Tywin could march north swiftly to meet Robb or west to relieve Jaime should he come under attack. In order to pin Tywin's forces on the Trident, Robb sent one army consisting of most of his infantry south along the Kingsroad whilst his cavalry crossed at the Twins and marched south to face Jaime.
The Stark infantry, commanded by Lord Roose Bolton, marched throughout the night in an effort to take the Lannister army by surprise. The Stark force was much larger in the book; numbering approximately 16,000 men and the Lannister force numbering approximately 20,000.
Ser Kevan Lannister commanded the center with lords Lefford, Lydden, and Serrett, a mixed force of pike and horse, Ser Addam Marbrand commanded the right with Ser Flement Brax and members of houses Crakehall and Swyft, all cavalry. Lord Tywin Lannister commanded the reserve. Ser Gregor Clegane commanded the left and the van, which included Tyrion Lannister. Lord Tywin put his undisciplined men in the vanguard, to tempt the Northern commander to over commit should they rout. He then intended for Ser Kevan and the center to wheel to the left and take the northerners in the side. However, the commander, Lord Bolton, proved to be cautious and failed to fall for the trap. Once he saw the battle was lost, he retreated in good order with only moderate losses. Roose's army positioned itself to make it difficult for Tywin to leave Harrenhal, and was later able to capture the castle once Tywin had left.