The beginning long-range muzzle loader shooter will soon learn that the single most important element in obtaining accuracy is consistency. If everything is the same with every shot there is no reason that all rounds should not go through the same hole. Of course this is humanly, mechanically, and meteorologically impossible, but the shooter can try his or her best to achieve the ideal. The most successful marksmen can replicate shot-to-shot conditions very closely, and their scores are proof that consistency works.
The second-most important element is finding the rifle, powder, bullet, and bore-condition combination that minimizes the effects of all the minute variations that cannot be controlled exactly. Barrel vibration and internal and external ballistics have an optimum load that makes the rifle predictably controllable and the bullet's flight both stable and well behaved. Finding this combination takes patience and care.
Perhaps the most helpful thing a new black powder shooter can do is listen to experienced shooters and follow their advice. The hard-won experience of others can dramatically shorten the time and effort needed to find the combination that works well in your rifle. A word of warning though: there are so many variables involved in black powder muzzleloader shooting that there are at least as many opinions about the best rifle, the best load, or the best hold as there are shooters. Pay attention to the better and more knowledgeable shooters and be polite to the others.
There is no better teacher than experience, and no other way to become experienced than to shoot. This shooter has found that much of the work of finding the optimum combination can be done at short ranges. If the rifle, load, and shooter can place 500-grain bullets ahead of 90 grains or so of powder in a tight group at 50 or 100 yards, then chances are that the combination will shoot well at 1000 yards. The longer ranges, of course, add the challenge of reading the wind, light, mirage, and other factors that only the really intuitive shooters master. These are the conditions where the shooter, the rifle, and the environment must truly become one.
Optimizing the accuracy of your rifle can be tedious, or interesting, or frustrating, or rewarding - which of these, the negative or the positive, depends on your attitude, your procedure, and your equipment. Fortunately, you, the shooter, have control of all three. The next few paragraphs offer a few suggestions, in reverse order, toward this end.
Always buy the best equipment that you can afford, even if that means obtaining your full kit only a bit at a time. Prioritize your purchases and use good sense. Clearly, you need a fine rifle, but the finest rifle cannot be fired accurately without excellent sights. Neither will it shoot well with poorly formed bullets or inconsistently measured powder charges. An engraved lock assembly does not enhance the rifle's accuracy, and a cleaning rod from Abercrombie and Fitch will not clean the bore any better than the same quality rod bought from your local gun shop. Much of your equipment can be made rather than purchased. You can make a powder drop tube out of copper pipe and some brass plumbing fittings and a funnel, or you can buy a beautifully machined and dreadfully expensive custom flared pipe.
Always be methodical when refining your load or shooting technique. Never change more than one variable at a time. The consequence of changing more than one thing at a time is that you will never know what made your shot group better or worse. Take care to keep everything consistent. Use a scale or a powder measure that has been proven to throw the same charge every time. Weigh all your bullets, and for serious shooting, keep only those that are within one grain of one another. Discard all bullets that differ very much from the norm; they probably have an internal defect. If shooting from a rest, always grip the rifle with the same pressure and rest the same part on the sandbag. In short, when testing a range of, say, powder charges, shoot as many identical rounds in exactly the same way as it takes to form a good idea how that powder charge groups shots. Then, change only the powder charge and repeat the process. The same change-only-one-thing-at-a-time holds for bullets, patching, wads, rifle rests or holds, sight apertures, or bore swabbing - you name it.
Always maintain a positive, enthusiastic attitude about your shooting. When you get tired, take a rest. When you get frustrated, quit for a while and do something else. If you are not enjoying your shooting, you will not shoot well. Always pay attention. A bullet with no powder charge can ruin your day as you try to get it out of the bore. Loading two bullets or a double charge is guaranteed to hurt, and, if you are lucky, the only hurt will be to your pride. If you do not give the sport your best shot, your best shot will not be one to be proud of.
In addition to serious shooting periodicals, the Internet is a great source of information. Do not be afraid to fess-up that you are a beginner. Real shooters who have something of value to offer and recognize a serious beginner will leap at the chance to help a fellow enthusiast. The Long Range Muzzle Loader mailing list is an excellent place to ask questions or just look at others "conversations".