How did it happen in the book?
Gandalf and Théoden with his men have arrived in Isengard and they go to talk with Treebeard. Aragorn, Legolas and Gimli stay behind with Merry and Pippin and they want to know what has happened after they parted at Amon Hen. First they have a comfortable moment eating and smoking pipe-weed and then Merry and Pippin tell what happened to them while they were captives of the Orcs and they tell about Treebeard and the Entmoot.
What happened when the Ents attacked Isengard is described here in detail through Merry and Pippin. They tell how the Ents marched to Isengard with Huorns and that they saw Saruman‘s armies marching away to fight in Helm’s Deep. Merry and Pippin stayed away from the events but they saw the Ents breaking the gates of Isengard driving Saruman into his tower and how Saruman didn’t know what to do when the Ents fiercely attacked the Orthanc. The hobbits found a place where to rest but they could hear how the attack continued and they saw Huorns all round Isengard finishing the Orcs. They also tell how the Ents broke the damns making Saruman’s machines stop and Isengard to flood and steam.

Merry and Pippin also say that Gandalf came to Isengard at the night of the battle of Helms Deep. He had urgent things to talk with Treebeard and this was the first time the hobbits saw him after he fell in Moria. Gimli wonders what happened to Wormtongue and Merry and Pippin tell that Grima rode to Isengard at the morning of the day in question. Terrified of what he saw he had tried to turn back but Treebeard caught him and Grima was now in the tower with Saruman. Everything else is now clear but Aragorn still wonders how there’s leaf from Southfarthing in Isengard and he plans to mention this weird thing to Gandalf also.

How did it happen in the movie?
This chapter as such didn’t make it to the movie. The basis of it, meeting of the friends, happens only in the beginning of ‘The Return of the King’ and when they meet they don’t spend time eating and telling their stories but they all immediately go to see Treebeard and Saruman. But the Ents’ attack to Isengard described by Merry and Pippin is shown in The Two Towers. And earlier in Fangorn Forest Merry and Pippin saw Saruman’s armies marching towards Helm’s Deep and when Treebeard called the Ents to the battle the hobbits saw the trees moving. In the end of The Two Towers there’s a scene where the hobbits find the food storage and the Longbottom Leaf that are mentioned in the book.

Changes
– Orcs aside, there are also lots of Men in Isengard but in the movie there seems to be only Orcs.
– In the movie Grima rides to Isengard before the battle of Helm’s Deep when he should have arrived there only after the battle.
– In the movie Gandalf sees Merry and Pippin already in Fangorn Forest and he obviously doesn’t drop in on Isengard before going to Helm’s Deep.
– In the movie a bit screen time had been given to Merry and Pippin as they participated to the attack with the Ents throwing stones from Treebeard’s shoulders while in the book they follow the events from a distance.

Borrowed lines
Treebeard’s “They have business with the Orcs” in the movie is actually Merry’s assumption of the events in the book when he’s telling how he saw the Huorns moving. The rest of the sentence “My business is with Isengard tonight. With a rock and stone” is Treebeard’s own line from the book.