Inigo Montoya is one of the most important characters in The Princess Bride, which is both a novel and a film, take your pick as both of them are classics.

Inigo grew up in the Spanish mountain village of Arabella. Arabella was high up in the hills above Toledo. In this little village lived the greatest sword maker the world had ever known, Domingo Montoya. Not that the world knew about him at all. The only people who knew of his talent were his son Inigo, and his lifelong friend Yeste. Domingo and Yeste had grown up together and both became masters at the art of sword making. Yeste chose the path of riches and became the most famous sword maker in all of the world. But from time to time someone would ask Yeste to make a sword that not even he could produce. When that happened, Yeste would take the job, and then head up to Arabella to see his old friend Domingo.

Once, just once, ride up and say, 'Domingo, I need a sword for an eighty year old man to survive a duel. Now that would be a challenge.

Without fail Domingo would refuse Yeste, and then there would be a great (but friendly) argument that played out exactly the same way each time. Eventually Domingo would agree to make the sword, but he would always make Yeste swear to claim the work as his own. This went on for many years, until one day a different man appeared and asked Domingo to make him a sword.

If I had a weapon to match my peculiarities, there would be no one in all the world who could equal me.

The man held up his hand, and Domingo saw that he had six fingers. The challenge of creating a perfectly balanced sword for a six-fingered man excited Domingo beyond all words. He slaved for a year to create the greatest sword since Excalibur. The six-fingered man returned and demanded the sword for a price of ten gold pieces, when he had already promised five hundred for it. Domingo refused him, and without a word, the six-fingered man slashed him throught the heart.

Inigo challenged the six-fingered man to a duel before he even managed to ride down the street. The six-fingered man won the duel easily, but did not kill Inigo, instead he cut him on each cheek. Scarring him permanently, giving him an eternal reminder of his place in the world. This did not sit well with ten year old Inigo.

Inigo went to live with Yeste, but he did not stay long. He soon left to study fencing so he could exact his revenge on the six-fingered man. For many long years he trained. He squeezed rocks to make his wrists strong, so he would never lose his grip on his sword. He would spend hours each day skipping, dodging, and sprinting, so he would be fast, lean and nimble. He studied with every master swordsman he could find. He studied with masters from icy lands, in case his duel was on ice. He studied with masters from the desert, in case it was hot on the day of his duel. He learned Agrippa, Capo Ferro, Thibault, Bonetti, McBone, and every other style of swordplay he encountered. When his training was finished he returned to Yeste's to ask if he was ready. Yeste was stunned, he proclaimed him the equal of Bastia, who was the last man ever to hold the rank of Wizard in fencing. Armed with that confidence, Inigo went out in the world to seek out the six-fingered man.

Hello. My name is Inigo Montoya. You killed my father. Prepare to die.

But alas, Inigo could not find the six-fingered man. It had been many years, and still he could not find him. For a while Inigo traveled around fencing local champions. It was good money, but he was just too good at it. Soon he was doing all of his fencing left-handed, but he was still too good for anyone to beat. The lack of a challenge got to Inigo, and he took to drinking. He eventually fell in with Vizzini and Fezzik and was hired to start a war with Guilder. This is where the The Princess Bride movie begins, and I shall go no further here, as I do not want to spoil this film for you.

The 1998 printing of the novel includes another scene from Inigo's past. It is in the "Buttercup's Baby" section that was added to the end of the book. This section shows a whole new side to Inigo, and is required reading for any Inigo fans.

Sources
http://www.devermore.net/surbrook/adaptionsbook/inigo.html
The Princess Bride 1998 printing
The Princess Bride DVD