How did Jack Sparrow end up making a deal with Davy Jones?

From the PotC wikia:

At some point in time, Davy Jones would strike a bargain with Jack Sparrow to resurrect his beloved vessel the Wicked Wench, which he would rename as the Black Pearl, in return for a hundred years of servitude aboard the Dutchman.

Also:

Beckett wanted to hit Jack where it hurts the most, so he set the Wicked Wench on fire as his men held Jack by, and made him watch his beloved ship burn. Jack was able to escape from the guards and tried to save the Wench from the flames, but instead was hit by a falling beam of the Wench's burning cabin. Jack found himself in a dream-like state, and, realizing he was dying, summoned Davy Jones and made a deal with the squid-faced captain.

From that same page:

• Davy Jones: "You've been captain of the Black Pearl for thirteen years. That was our agreement."
• Jack Sparrow: "Technically, I was only captain for two years, then I was viciously mutinied upon."
• Davy Jones: "Then you were a poor captain, but a captain nonetheless! Have you not introduced yourself all these years as Captain Jack Sparrow?"

To elaborate on the answer to this question Jack worked for the East India Trading company under Beckett when he was asked to sail an outdated ship. The deal was that the ship would be sold to jack for one shilling after he had delivered the cargo.

This cargo was 100 human slaves.

During the delivery Jack realized he could not complete it and freed the slaves. Because of this Beckett ordered the ship, the Wicked Wench, to be burned while Jack watched. While the ship was burning Jack tried to save it, nearly dying and making a deal with Davy Jones who resurrected the charred remains as The Black Pearl making Jack Captain for 13 years.

After those thirteen years when Jack attempts to free himself from the deal he is given the choice of sacrificing 100 human souls to save his own, the same number of human souls he once freed.

This is revealed in a small yet clever bit of dialog in At World's End between Beckett and Jack.

• Becket: "We had a deal, Jack. I contracted you to deliver cargo on my behalf, you chose to liberate it."

• Jack: "People aren't cargo, mate."