At the very beginning of Homer's The Odyssey, in Book I, the author references the figure of Calypso, the daughter of the powerful Titan who seduces Odysseus and essentially holds him captive for years, impeding the heroic veteran of the Trojan War's journey home to his loving wife Penelope. In this opening section, titled "Athena Inspires the Prince," the author wrote the following regarding Odysseus and Calypso:

"But one man alone … his heart set on his wife and his return—Calypso, the bewitching nymph, the lustrous goddess, held him back, deep in her arching caverns, craving him for a husband."

As readers of The Odyssey discover, however, Calypso is indeed compelled to release her hold on Odysseus, and the instrument of the mortal's liberation is Athena, the goddess who looks out for Odysseus during the many years he spends on his journey. Athena is the daughter of Zeus, the most powerful figure in Greek mythology and in Homer's story. 

In Book V, "Odysseus -- Nymph and Shipwreck," the story of the chapter's titular character and of his bondage by Calypso is continued. In this section, Homer describes Athena's pleas to Zeus to intercede in Odysseus's behalf, despite her own manipulations of the mortal's trials and tribulations. Athena approaches her father as the mighty Zeus sits surrounded by gods on the occasion of this council:

"Athena began, recalling Odysseus to their thoughts, the goddess deeply moved by the man’s long ordeal, held captive still in the nymph Calypso’s house: “Father Zeus—you other happy gods who never die . . . Think: not one of the people whom he ruled remembers Odysseus now, that godlike man, and kindly as a father to his children."

Zeus responds to his daughter's plea on behalf of Odysseus by dispatching Hermes to deliver the message to Calypso that Odysseus is to be allowed to continue his journey home to his wife:

“You are our messenger, Hermes, sent on all our missions. Announce to the nymph with lovely braids our fixed decree: Odysseus journeys home—the exile must return."

The answer to the question -- who helps Odysseus escape from Calypso -- is Athena and Zeus, with Hermes serving as the messenger. Athena, as noted, watches out for Odysseus' welfare, a particularly onerous task in the face of the powerful god Poseidon's efforts to the contrary. Athena's relationship to the most powerful god of all, her father Zeus, is sufficient to sway events in her favor.

This is a good question and I can see why you ask it. If we look at the Homer's work carefully, we must conclude that Odysseus does not escape Calypso's island. He is let go by Calypso.  

More specifically, the gods allow him to leave. Zeus concludes that it is time for Odysseus to set sail for home. When this decision is made, Zeus sends Hermes on his way to Calypso to tell her to let Odysseus go home. She does so unwillingly, but she really has no choice, as the king of the gods has spoken.

Calypso, therefore, helps Odysseus by giving him some supplies to make a sail and off Odysseus goes.