I'll try to summarize:
A big discussion comes down to what your purpose and thought is with the muzzleloader. Some guys like the traditional aspect of it- using older style guns, flintlocks, and balls. Other guys use slightly newer methods using percussion caps (which are like a primer on a cartidge) and balls, or maxi-balls. A maxi-ball is a more conical designed bullet that generally carries much more energy farther downrange, and usually is more accurate since it engages the rifling better and has better rotational energy- I'm not sure if that's the correct term, but it has a better ballistic coefficient- it's longer but the same diameter. Other guys use saboted modern bullets, like from a .44 or a .45, and these are generally the most accurate.
Then you get to the modern muzzloaders- they are usually in-line with a shotgun primer at the rear and use non-sulfur powders either in pellet form of powder form. The sulfur in traditional blackpowder or even lesser amounts in Pyrodex are pretty caustic causing rust to easily form. The problem is that non-sulfur powders (like Triple7 or pelletized powders) are generally harder to ignite, so a standard percussion cap might not set it off under more extreme conditions, like high humidity. The shotgun primer creates way more directed heat to ignite better.
The pellets (image link:
https://media.midwayusa.com/productimages/880x660/Primary/441/441251.jpg) are usually 50 grains each with a hole down the middle. That way when the primer goes off it fires down the middle hole igniting the powder more evenly promoting a more consistent charge and better accuracy. At least that's the idea.
Most .50 caliber muzzleloaders run around 100 grains of powder, either measured out with a powder measure then poured in, or two pellets are dropped down the barrel. Magnum muzzleloaders can use 3 pellets (150 grains).
My modern magnum muzzleloader uses 3 triple 7 pellets (150 grains), a modern saboted .44 high performance pistol bullet, and with a rest can group a 3 shot pattern in a half-dollar at a hundred yards. It's good out to about 200 yards, my longest shot was about 170.
With a muzzleloader, obviously you load down the muzzle. How you do that depends on a few things.
Some guys are real traditionalists- flintlock (as Black Hills mentions, nostalgic but a PIA) only. A flint lock uses the sparks of flint striking steel to spark the finer powder in the pan, which follows a hole into the breech where the main charge lies. To load this weapon, you pour the powder down, then add a patch over the end (usually greased somehow), then slide the ball in. You push it home with the ramrod. At that point some guys slam the rod home until it gets a bounce- letting you know it is firmly seated. Other guys push it in all the way and have a mark on the rode so you know when it's down all the way.
The problem with the ball, is that while it is traditional, it is fairly inaccurate and loses energy quickly. Hence the maxi-ball or saboted bullets.
What you use kind of depends what you are after. I'm pretty much looking for more time in the woods and more venison, so I usually use my magnum muzzleloader, a Thompson/Center Omega with a bullet-drop compensating scope that is made for that load. I also have a Thompson/Center Grey Hawk- a traditional-styled side percussion powder loader, but even in that I use saboted bullets of less weight on front of 90 grains of Pyrodex (that has been the most accurate load with that gun). I use that once in awhile and have taken a few deer with it. With that gun I am good to about 100 yards, but it has iron sights. I usually use it in close-quarters hunting, like brushy areas.
They also make them in larger calibers (.54) or smaller calibers (.45 and smaller for small game).
Once you shoot one a few times, you get pretty proficient at loading, and as Wesley mentioned,it's not a big deal. I can probably reload in less than a minute.
I'll attach a video of me shooting a deer with the muzzle loader below:
You'll note the vast amount of smoke with a muzzleloader. Generally you lose sight of the deer, especially if it's at any long range. Of course 777 and pyrodex create far less smoke than real blackpowder. That really fires out a cloud.
