Tools: On barrel cleaning, find (1) a jag that fits the bore, (2) a scraper to clean the breachplug, (3) a worm and since you're at it, (4) a stuck ball remover. Get (5) a solid brass cleaning rod (black powder people like Tipp Curtis has them). The worm is used to retrieve a patch that gets stuck in the bore. The stuck ball remover is like a wood screw that is attached to the cleaning rod and is used to bore into the bullet to withdraw it (note: there are better ways to remove a stuck bullet but that's for later).
Firearm Safety: First rule of firearm safety is keep the muzzle pointed in a safe direction. Second Rule of firearm safety is Keep your finger off the trigger and on the stock when handling it. The next thing check to make sure it isn't loaded. Insert the ramrod down the bore until it hits the bottom. Mark the rod with a pencil line or tape. Remove the rod and lay it alongside the barrel. If the end of the rod is near the nipple, your gun is unloaded. If it is a little distance away, it has something in the barrel (and may be loaded).
The safest way to remove a lodged in object is with a CO2 discharger. It takes a regular CO2 cartridge with an adapter that slips over the nipple. Pushing down on the discharger sends a blast of air into the barrel that should dislodge the ball. When you do it though, make sure the muzzle is pointed in a safe direction. My classmate took out a vase that his mother-in-law gave his wife. Oppski! So, if there's an obstruction and you use the C02 discharger, be sure it's pointed in a safe direction where the discharged object won't damage anything. If the CO2 discharger won't dislodge the stuck object, then put the stuck ball remover onto the ram rod and push it down the barrel. Twist the ramrod to bore the stuck ball remover into the ball. Then pull it out. Had to do this last week for one of my students.
Cleaning the bore: The key tool is the jag that is snug to the bore but loose enough to attach a cotton cleaning patch. Never use patches made with synthetic material. Pure cotton only. For a cleaning solution, normally one uses hot soapy water. In this case, I would rather use Ballistol, which is a German made product that both cleans and lubricates. Put a bit of Ballistol on a patch (I use a sardine tin to hold my liquids) then place the patch on the center of the bore. With the jag attached to the cleaning rod, push it straight down the barrel and pull it out. The patch should come out with the jag. Inspect the patch. The bore is likely dirty for dried oils. Get a fresh cotton patch dipped in Ballistol and repeat until the bore is clean. Then push down a dry patch.
If the patch should slip off the bore, then remove the jag and attach the worm (it's like the field artillery worm used in the Civil War). Drop that down the bore and spin the cleaning rod several times to "hook" the patch. Then pull out the cleaning rod with the patch twisted onto the worm.
The gun dealer may try to sell you a bore brush. Do not buy stainless steel or brass/bronze bristle bore brushes. Stainless can harm the bore so they're a no-no. Brass or bronze brushes scrub well, but are designed to be pushed through the barrel and then pulled back out. If you stop midpoint and pull it out, the bristles will lose their flexibility and their scrubbing powder. Because muzzle loaders like the one you have don't allow the brush to be pushed through, don't waste your money. If you must buy a bore brush, buy a nylon one. They're more flexible and less susceptible to being ruined in pushed halfway in and the pulled out.
If you never plan to shoot it, then get Renaissance Wax, apply it to a patch and push it down the bore. Push a couple of dry clean patches down the bore after that to polish it and remove any excess wax. You may treat the exterior of the barrel and any exposed metal and wood with the same Renaissance Wax. If you plan to shoot it, then a light coat of modern gun oil may be rubbed on the metal. If you live in a high rust environment and plan to shoot it, then RIG Gun Grease may be applied on the exterior metal.
The NRA & National Muzzle Loading Rifle Association have jointly issued a book, NRA How To Series: Muzzleloading, on the use and care of muzzle loading firearms. You may want to check out if there is a muzzle loading class somewhere. Go to NRAInstructors.org to see if there's a class. If member Johan Steele was nearby, he'd be my choice of teacher for muzzleloading basics.