There are several ways to get a BJJ Black Belt. Various ways have proved to have varying levels of success. The fastest, is of course, to mimic what Jay Queiroz did and fake himself as a Black Belt under IBJJF. Disclaimer: you might get exposed and shamed on the internet.
Seriously, don't do this shit. Don't even fake the lower belts, the distinction and differentiation is as clear as sub-50 PSI air.
Admittedly, there are several new avenues of practicing BJJ in this day of digital age. One infamous way, is to do video techniques shown through an online subscription (e.g. Rener Gracie in www.gracie-university.com). While this manner of learning has been widely disputed, and heavily criticised, there is still a certain amount of legitmacy to it, abeit the inclination that it looks dodgy. I've personally watched a couple of the free videos, and I must say that, to be able to see a technique from various angles repeatedly does aid in learning. But even Rener Gracie himself mentioned in the subscription that one would still require a physical rolling partner or a academy to fully appreciate the art.
In general, BJJ has 5 belts. There is a red-coloured coral belt that is reserved for those who have a very (extremely) deep black belt, and the founders of BJJ (think 7th degree and above). But for the general populace like us, the belt chase is mostly for the 5 colours above. We start at white, and we progress.
So how long?
Well, it depends. There are a varying combination of factors leading up to this. If you read around martial arts forums, or google deep enough, you'd easily find that the average person would take around 10 years to achieve the black belt. The number of years is not an absolute, and is dependent on your mat time, talent, achievements, etc.
What if I'm really talented and I'm going to roll/train everyday?
The fastest widely recognised legit black belt in BJJ is BJ Penn (former UFC fighter, UFC Hall of Fame), and he did it in 3 years. In those 3 years, he has also attained medals in various IBJJF competition. There are also a couple of other 3 year black belts, you can read more on them here.
Comparing BJJ with other popular belted sports
BJJ belt progression is a long journey, at least for the average folks. The chart below details generically the timeline of progression for BJJ belts:
Instead of counting the number of years, there also has been internet folks that have been estimating the amount of mat time put in towards the journey to the black belt. The power of the internet estimates the number to be around 4,000 hours (some less, some more). But let's take 4,000 hours as best estimate:
Assuming you're rolling 2 hours a day, 3 times a week = 6 hours/week
To reach Black Belt = 4000 divided by 6 = ~670 weeks = ~13 years
Assuming you're on form, and roll 5 times a week = 10 hours/week
To reach Black Belt = 4000 divided by 10 = 400 weeks = ~8 years
Losing steam? Watch and hear it from the Miyao Brothers below. The Miyao Brothers are young black belts that are known to spend almost every minute of their waking time breathing, training or teaching BJJ.