The very shortest version I can come up with:
Typically, a .45 caliber rifle will use a pure lead round ball of .440" in diameter. Some guns might want something slightly different, and some shooters prefer a tighter or looser fit, but very generally speaking, .440" should work.
The way to be absolutely sure is to slug the bore. This involves pounding an oversized slug into the bore, retrieving it with a screw, and measuring it. This may not be something a new muzzleloading shooter wants to try, but if you do, I'm sure you could get good information here.
The round ball needs to be wrapped in a lubricated cloth patch for loading. There are a zillion opinions on how to do this. Probably the easiest way is to order lubricated "Wonder Patches" in size .45. They are available in several thicknesses so that the shooter can achieve the desired fit. This is another area with a zillion opinions. You probably would be fine with a medium thickness, .015" or so.
Some people like to use a wad between the powder and the patched ball. It is not necessary, but in some cases it can improve accuracy and ease cleaning. If you decide to, again it probably is easiest to order pre-lubed wads in .45 caliber.
Real blackpowder is probably your best bet. In a flintlock it is the only thing that works reliably. In your caplock the substitutes should work as well. The proper granulation is 2fg. Traditionally, a light load would be equivalent to the ball diameter (45 grains) and a max load would be double, 90 grains. These rules are essentially old wive's tales, but they do work, more or less. If you want, you could simply go for 60 grains or thereabouts and then give it no further thought.
You are the only one who can tell which caps are right. Chances are that #11s will work. CCI #11s seem to be slightly loose on a lot of guns, but if they are, giving them a little pinch causes no problems on a single shot gun.
Process:
Wipe the bore down with a patch. Fire a cap to clear the vent*. Measure powder into a
measure and not directly from your horn/flask/can, and pour it down the barrel. Run a wad (if using one) down on top of the powder with a ramrod or loading rod. There is no need to tamp down hard or bounce the rod. Then center a patch over the muzzle. Place a ball on it. If it is a very tight fit you may need to use a
short starter to get everything into the muzzle. Then use the ramrod or loading rod to push the ball down firmly onto the powder. Finally, cap the gun and fire.
After firing, some people will simply reload, as above, and keep going until fouling makes seating the ball too difficult. Other people like to run a brush and/or a lubed patch down the bore between each shot to ensure ease of loading and a consistent shot-to-shot bore environment.
After shooting is concluded the gun does need to be cleaned, hopefully within a few hours. I'm not going to open that Pandora's box here, but there is more than enough information available on the topic both here and on the internet in general.
Enjoy!
<edit> Shopping list:
In addition to the short starter and powder measure, consider these items.
If the gun does not have a ramrod, you will need one. If it has a wooden one you might want to get a
steel loading rod. These are easier on the hands and a lot less likely to break. They are not an absolute necessity, though.
Chances are you will need some tools for the end of the rod.
A
button jag is good for loading, and can be used to hold a patch for cleaning as well. In my experience they sometimes will drop the patch off at the breech, though, so I prefer to wrap patches around an undersized brass brush. If you do lose a patch, you'll want a
worm attachment to fish it out. Note that ramrod accessories come in two common thread sizes, so you'll need to get that sorted before ordering.
Most shooters use a flask or horn to carry their powder. Some folks just use a
spout which attaches directly to the powder can. It is generally considered unwise to pour directly from the can/flask into the bore, as at least theoretically a spark can linger in the breech and set off the whole can. You will definitely want a powder measure such as the one linked earlier.
I think that's it for a bare-bones experience. Most of us who get the bug will load ourselves down with all sorts of nonsense, but unless I've forgotten something, I think the above list will get you through your first outings.
*This really ought to be done at the range, with the rifle pointed at a safe target. Unless you have absolutely proven to yourself beyond doubt that the rifle is not loaded, well...