I have the Sharn sourcebook and there's so many different districts, wards, and places that I'm not sure I can keep all of this info straight.
I haven't run a specific Sharn adventure but ran numerous games in similar metropolis environments. Among them Waterdeep, Laelith, Paris By Night for VtM and so on.
The most important thing is to go one step at a time. Don't try to explain everything at once to your players. Think in terms of characters/real life individuals: when you arrive in a city, what do you see first? That may be its main gates in a medieval city, or the landing grounds/lightning rail stations of Sharn. Describe them. Then, have an encounter with an official of the city. A guard, a blunt sergeant of the watch, something like this. Give "color" to the city through this NPC. Perhaps in Sharn this guard would be a lesser son a noble family of the Upper City wondering what the hell he is doing here, thus showing disdain and impatience towards the PCs? Or perhaps it is an old scholar for Mortgrave university?
The point is this "first NPC" is the first meeting of the PCs with a local, so make it count to get some points about the global nature of Sharn across: there are wards, there are levels in this city, and huge social disparities between inhabitants of different wards, levels, areas. Also tell about all the legal stuff through this NPCs. Like you are not allowed to draw weapons and cast spells in the street, you need identity papers to access some areas in the city, and so on.
When this is done, describe what the PCs see when they get out of the station/gate. What feeling does the view inspire to the PCs? What does it look like? How does it smell? Et cetera.
Ask then what their intentions are. Like "We go to an inn". You answer "You see a small inn nearby..." with a local description following, and then tailor the PCs through their meetings in there. Perhaps they'll be able to find/buy a rough map of the ward they're in, or even a basic overview of the city drawn "live" by the innkeeper as he explains some stuff to the PCs? One step at a time.
Does it help?