Good question.
 
In a typical GM plant, cars come off the end of the line at 55 an hour.
From a dealer standpoint, we have ordered a new Buick and had it delivered to us off the truck in as little as 10 days.  That is the exception, and probably the factory needed orders badly, so they actually started to build the car before they even got our order for it.
If nobody had ordered it, it would have been built and sent to a regional warehouse, and the "factory men" (District Sales Mgrs) would then have to get on the phone and try to cajole their dealers to help them out and take a couple more cars (that are already built and in storage).
As a car is going thru the process of being built, its many components and sub-assemblies may be made in locations far away from the final assembly plant.  Dash assemblies, electronic components, wiring harnesses, gas tanks, brake parts, seats, carpets, tail lights, etc etc.  They all have to be built and and sub-assembled and shipped on a very precise time schedule, so they reach the assembly plant (like Fairfax), only minutes before they are needed. It's called "Just-in-time", and the Japaneses are the ones who came up with it, to save money. 
So at the assembly plant when a certain car is destined to be assembled at an exact time, first the frame starts moving on the line.  The tires are unloaded from the railroad box car that comes right into the plant, and they are stacked in the exact sequence so the right size tires are mounted onto the exact wheels and sent on to be mounted onto the car.  Basic components are mounted to the frame, and the body has to be perfectly timed to meet the frame and be bolted to it, as it travels down the line.   Each component in turn meets the car, and is assembled to it.  Each part has to be the exact correct one for that particular car. 
Now back to the original question.  As the dealer,  I order the exact car my customer wants.  Up until the time the body gets painted, the color can be changed to match my order.  Up until the time the interior trim color and quality choice must be specified, I can change it to match my customer's wishes.  Same with the sound system, and all the options, etc.   So when I ordered that car that only took 10 days to get, much of the car was already built, and the factory compared my order to what was in production and un-spoken-for, and did a match-up.
Someone did a study a few years ago, and decided GM could build 100,000 cars, with every one of them being different from all the rest, because there are so many combinations of options.
If you stop and think about it you'll conclude that it can't be done.  Yet every day Fairfax cranks them out at 55 per hour, and they are beautiful and almost perfect.  Impossible, but there they are.
 
When I was the Buick "factory man" for NY City,  I would drive to work down the West Side Highway, and I would look at all the tall buildings, the heavy traffic, and  everything that goes on in New York City every day, and I'd say to myself, "This is not possible".  Yet every day it functioned.  Millions of people did their job, went home, and we all made it thru another day.
 
The same thing applies at the Fairfax Assembly Plant.  Every piece of a new LaCrosse, every nut and bolt, every stitch in the upholstery, every connection in the wiring harnesses, every person on the line, everything comes together at the exact precise time, positioned and tightened to the exact torque, installed exactly in the right place, and at the end of the line, the next driver jumps in, turns the key, and it starts. He drives away to the storage yard, where the repair crews will read the inspection ticket that tells them what the inspectors said about the car.  They will take care of the imperfections before the car is shipped.  Maybe a little scratch from an "OOPS", maybe a defect in the windshield glass that will have to be replaced, maybe a seat trim that doesn't match the car.  The final repair people are skilled in everything, much like the people in a dealership who have to fix whatever is wrong.
 
So the long answer to your question is, it takes years, it takes months,  and it takes a couple of hours to build a new LaCrosse,  depending on how far back from the final drive-off at the end of the production line you want to go. 
 
How do I know all this?
I can show you a picture of me at age 5 looking under my dad's Buick, trying to see how it works.
In High School I was the only boy who some of the mothers would let their daughters go to out-of-town ball games with.  I worked hard to keep that reputation, and I always had a car full of good lookin babes.   Never ever an accident, ever.   Even to today.
I graduated from The Ohio State University, with a degree in Marketing in preparation for the future.  (GO BUCKS!)
I graduated from General Motors Institute in Flint Michigan, where I sometimes worked on the production line at the Buick plant, to prepare for the future. (Go Bulldogs)
The U S Army made me an Electronics Instructor for 2 years, and finally Buick Division of GM  made me their Factory Man for NY City. 

Many times I had to go to various GM plants to get quality problems fixed as quickly as possible

And finally I got my life long dream of being a small-town Buick dealer. 

I'm still part of  a weekly conference call with  the biggest and best of the Buick dealerships nationwide, still pursuing  reliability and quality control concerns on the cars being built today.  Having a hand in contributing to Buick's reliability and quality control reputation is more than satisfying.  It's a way of life.   At assembly plants (like Fairfax), the quicker we fix potential problems, the better.  Helping to keep little problems from becoming big ones is what we do.  

   So the next time you see a new Buick, think of all that went into it, and all of the dedicated people who spend their life making it a great car.