The Odyssey begins in medias res, "in the middle of the action."  Homer begins near the end and reveals much of Odysseus' adventures via flashback in order to compress time and build toward the climax of the suitors' fates on Ithaca.

In the story proper, we first meet Odysseus on the island of Calypso, his last stop before he washes ashore on the Island of Phaecia, where he narrates his odyssey to King Alcinous.

Depending on how you number Odysseus' stops on his journey, The Odyssey begins at about number 12 (Calypso) and then moves forward to number 13 (Phaecia).  Then, it flashes back to the beginning, number 1 (just after the Trojan War).  It moves from numbers 2 through 11 before resuming again back at number 13.  Then, Homer finishes Odysseus vengeance at Ithaca, stop number 14.

This is a very broad question, because Odysseus has gone through so much that there are many starting points to which  we can point. For example, we can speak of Odysseus at the Trojan war and how he was pivotal in the Greek army and how he helped them to win the victory against the Trojansthrough the ploy of the Trojan horse. We read of this in the Iliad of Homer. Or we can speak of Odysseus in his voyage homeward and his struggles along the way. We read of this in the Odessey (again written by Homer). If you want an exhaustive view of Odysseus, read both works.

Where is Odysseus when he begins to tell his tale?

Odysseus tells his tale at an enormous feast held in his honor by Alcinous, king of the Phaeacians. Normally, the Phaeacians are not renowned for their love of foreigners, but the goddess Athena, Odysseus's divine protector, intervenes to ensure that he receives a warm welcome. Once Odysseus arrives at Alcinous's palace, he proceeds to tell the king and queen about his predicament. Alcinous kindly responds by offering to provide Odysseus a ship for the next stage of the voyage.

As an honored guest, Odysseus, who still hasn't revealed his true identity, is treated to an entertaining display of games such as boxing, wrestling, and discus throwing. Odysseus is happy to watch rather than participate, as he doesn't want to give himself away. But after being insulted by a young athlete, Odysseus can't resist putting him in his place and promptly shows up the impudent young pup by beating him in a discuss throwing contest.

Later that evening, the Phaeacians throw a big feast in their guest's honor, and it is here that Odysseus finally tells his tale. He's inspired to do so by the beautiful song sung by the minstrel Demodocus about the Trojan War, in which Odysseus played such an important part. Overcome by emotion Odysseus breaks down, causing Alcinous to ask him who he is, where he comes from, and where he's going. It is then that Odysseus embarks upon the telling of his epic tale.