One way I did it was to give each character a level 1 warrior goblin, and have them chased through the streets of sharn by a bugbear who wanted the Mystery Shiny one of the goblins had. They eventually ran into a tavern to hide, blending in with other goblins and hiding behind the various bar patrons. The bugbear chased them in, beat them all to within an inch of their lives, but the character with the Mystery Shiny managed to escape (by lighting the bar on fire with alcohol). After the ruckus was done, the characters were revealed to be some of the patrons who sat by watching the whole affair as though it were everyday life in Sharn.
The other way I started the campaign was with a character being from the Morgrave University (the adventurer's academy) basically being given his final project to graduate: "Compose an adventuring party and successfully return to Sharn with an item of significant value within three weeks." As the character was played, he was a bit of a bungler who did poorly in his classes, fell asleep through the dwarven professor's lectures on party tactics and the lessons on proper techniques for thoroughly searching a door for traps.
Given his reputation and his laid back approach, by the time he started searching, just about everyone in the graduating class had already formed up into groups. Some even suggested he go to the University Bar, as there's always something on the community boards for adventuring. There he found only a few advertisements for some members of the University's Bard Academy (our group detests bards as a running gag), and so he set out into Sharn, looking for a group. He found the various party members by chance (a newly reactivated warforged, a down-on-his-luck with bills to pay dwarven P.I. named Flint Bourbon [who was the only dwarf living in Goblintown], and an elven monk from House Thuranni).
