Answer:
It was actually Helen of Sparta, not Troy, who went with Paris of Troy, leaving Sparta, her husband and daughter, and everything she was behind. She didn't actually become Helen of Troy until such time as she was welcomed into Trojan society as a Princess of Troy.
Helen of Sparta, wife of King Menelaus of Sparta, wasn't actually kidnapped by Paris, a Prince of Troy. Helen had been promised to him by the Greek goddess Aphrodite, whom Paris had claimed was the most beautiful of all the goddesses. Naturally, like most women, this pissed of the other goddesses, Athena and Hera. Paris went to Sparta during a period when Menelaus was absent from Sparta for a funeral.
True to her word, as Aphrodite had promised, Helen fell in love with him and willingly left Menelaus and Sparta behind, along with Hermione, their 9 year old daughter (bet you didn't know where the name Hermione came from).
At this point there are conflicting testaments as to whether or not Paris and Helen actually went to Troy; some accounts have them going to Egypt, where upon learning what they had done, seized all the treasure that Paris had taken, including Helen, and waited for Menelaus to show up and reclaim his wife and gold.
By this time, Menelaus was home in Sparta, had been informed that his wife had dumped him for Orlando Bloom, and left him a lot poorer and with a kid to boot. He was not a happy camper. Having promised Menelaus that they would stand by him should Helen ever be abducted again (she had already been taken before, once when she was only 12) her former suitors, who became the Greek heroes of the Trojan War.
After getting to Troy and demanding the return of Helen and his loot, as stated previously, some accounts had Helen and Paris in Egypt, so when the Greeks showed up on the Trojan beach, King Priam of Troy (Paris' Dad) and Prince Hector (Paris' brother, and hero of Troy) told Menelaus, Odysseus, Ajax, Achilles, and all the other Greeks who had shown up for the war that they had been suckered - Paris and Helen weren't there at Troy, but had in fact eloped to sunny Egypt for a few quiet years while things "died down" a bit.
Well, things died of course - the Trojan War lasted 10 years, the Greeks unable to penetrate the high, steep walls that had kept them from getting inside the city. At that period in history, there were no great siege machines of war, Trebuchets, Catapults, or anything for breaching battlements.
After 10 years, the Greeks got tired of not winning every day, and losing their friends all the time, not to mention the deployment time away from Greece. 10 years is a long deployment. Sitting around the campfire on the beach one night, Odysseus comes up with a brilliant plan - let's build a wooden horse, hide a bunch of us inside, and send everyone else away. The Trojans just might be dumb enough to bring it inside the city to offer it to Poseidon at their temple, to rob us of OUR offering to Poseidon on the beach for a safe journey back to Greece.
So the Greek fleet sails just out of eyeball range, and leaves the wooden, hollow horse offering thingy on the beach with a lot of stinky Greek dudes inside. Not only is it cramped, it's also hot as hell, and they can't make a sound or move for fear of being discovered by the Trojans. And we won't even discuss what they did to relieve themselves during that period.
Anyway, you know the rest - the Trojans fell for the stupid trick, and dragged the horse into the city, partied all night and got falling down drunk. At which point by that time, the Greek ships had sailed back, and Odysseus, Achilles, and the rest of the Greek gang had slithered out of the horse and signaled their buddies on the beach that the Trojans had fallen for it, and that the gate was open. In other words, they signaled "Time to Rape, Pillage, and Plunder."