How did the clones land at the battle of Geonosis?

Question

In Star Wars Episode II: Attack of the Clones, we see the Cavalry (warning: TVTropes link) arrive in the form of the clone army led by Master Yoda. However, just a few scenes later as Dooku is escaping into space, we only see Trade Federation ships. My question then is: how did the clones arrive at the battle on the surface?

Answer 1

The film's original script contains some useful info, including several scenes that were written, but not filmed.

I've highlighted the relevant portion:

YODA: Come on - hurry! Hurry!

The SURVIVING JEDI dash to the Gunships and scramble in. MACE WINDU hangs on tight as the Gunship, firing all its weapons, rises out of the arena up and over the topmost rim.

EXT. GEONOSIS, TERRAIN OUTSIDE EXECUTION ARENA - DAY

The massed lines of parked Federation Starships and the DROIDS surrounding the arena, are themselves surrounded by thousands of Republic Starships, disgorging TENS OF THOUSANDS OF CLONE TROOPERS. Beyond, more Republic Starships are landing and spewing out troops.

INT. GUNSHIP NUMBER ONE - DAY

MACE WINDU stares at the incredible sight.

So the answer is that the clone-troopers who arrived at the arena traveled there in gunships and the majority of the troops who landed, traveled there in Republic Starships, which you can clearly see in several of the background scenes

Answer 2

According to the official novelisation, as referenced on this Wikia page:

huge Republic assault ships penetrated the upper atmosphere and dropped a fleet of gunships, carrying thousands of clone troopers and dozens of AT-TEs as well as Jedi General Yoda, to the surface.

The word "gunships" is a link to the page on Low Altitude Assault Transport:

The Low Altitude Assault Transport (LAAT), also known as the LAAT-series gunship nicknamed "Larties" by some clones, was a gunship series used by the Grand Army of the Republic during the Clone Wars. The series was produced by Rothana Heavy Engineering.

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Actual quote from the novelisation (big thanks to @DVK):

"Then I'm sorry, old friend," Count Dooku said, in a tone that didn't sound at all sorry. "You will have to be destroyed." He raised his hand and looked to his assembled army, prepared to give the signal. But then Padm, exhausted, dirty, and bloody, raised her head to the sky above and shouted, "Look!" All eyes turned up to see half a dozen gunships fast descending upon the arena, screaming down in a dusty cloud about the Jedi, clone troopers rushing out their open sides as they touched down. A hailstorm of laserfire blasted the new arrivals, but the gunships had their shields up, covering the deb arkation of their warriors.
[...]
Mace could hardly believe the incredible sight unfolding before him, as thousands of Republic ships rushed down on the assembled fleet of the Trade Federation, dropping tens of thousands of clone troopers to the surface of the planet. Behind him, Yoda continued to orchestrate the battle. "More battalions to the left," he instructed his signaler, who relayed it out to the field commanders. "Encircle them, we must, then divide."
_{-- R.A.Salvatore, "Attack of the Clones" novelization}