No one seems to have mentioned
Marksmanship Principles. These are what allow you to hit anything with anything. These principles apply to all small arms, chassis mounted included. Essentially these principles are easily broken down into categories.
Breathing.
Natural Point of Aim.
Support.
Trigger Squeeze.
Breathing
This is fairly straightforward in my opinion. The breathing in this case relates to the movement of the weapon in regards to you drawing breaths. An obvious fast paced breath will cause the rifle to rise and lower as you inhale and exhale respectively. A slower breath rate will of course diminish this effect, and holding your breath will temporarily halt it. Through my experience I've found it useful to inhale for 4 seconds, exhale for 4 seconds, with 2 second pauses in between. This controlled breathing will help lower your heart rate and will allow you to predict when the sight of the weapon will rise and lower in respect to the target. Skillful individuals, typically snipers or the ilk, also train to fire between heartbeats; or so I've been told. I personally have tried this with little success.
Natural Point of Aim
A Natural Point of Aim is by far one of the most important aspects of accurately firing a weapon in my opinion. To find your NPA (Natural Point of Aim) the tried and true method is to aim your sights on a target, close your eyes and lower the weapon, then without opening them raise it once again. If it is on the same target, at the same position, you've achieved a NPA. This is exceptionally important for repeated firing of a firearm as after the initial recoil the sights will want to set themselves back onto target. If you don't have this NPA then your muscles will have to push the weapon onto the target which causes fatigue, and upon firing, can cause a shot to go astray or be pulled in some cases. The easiest way to achieve a NPA is to find a comfortable position where your muscles are not struggling to hold the firearm, but support it. If you hold the firearm in position for a minute, you should not be shacking from fatigue, nor should your muscles have any stress on them. This isn't always possible, such as in a gunfighter pose, and so sometimes you have to take a partial NPA due to your fighting posture.
Support
Support (steadiness & control) and a NPA go together in that if you have no support for the firearm, it will not stay in your hands, and you won't ever want to rest on a target. I've seen this firsthand after someone nearly shot 4 others because they had poor control and support of their rifle. There is no golden rule for supporting a firearm that I've found. In theory the best method is create triangles in your body, such as resting an elbow in against your ribs while your hand supports the stock of a rifle. Again though, if the stance isn't comfortable, or strains the muscles, you'll gradually begin to lose support and control and your rounds will not be fire accurately anymore. In a chassis mounted system the mechanics are normally sufficient to act as the support for a firearm, however it is wise to apply a good dose of butt pressure to prevent the muzzle from moving wildly under rapid fire.
Squeezing the Trigger
By golly gee if this wasn't it's own little bit, it damn well ought to be an article of its own. Squeezing the Trigger refers to how you actually engage the trigger. Though Hollywood may have people believing that you pull with your finger, you actually want to make a very gradual and controlled squeezing motion, almost to the point where your rifle, pistol, or what have you, surprises you when it shoots. With experience you'll know exactly when it will fire, but the principle remains. The reason this is so important, is that if you jerk, pull, or otherwise engage the trigger too quickly it may move the position of the rifle in your hand, shoulder, or on the ground. This will cause a pulled shots. Pulled shots have a tendency to miss. As you gain experience even rapid fire and short full auto bursting fire becomes more accurate as you squeeze the trigger, at least mine has.
Those are your basics for Marksmanship Principles. I may not have explained them the best, but hopefully I've done enough to help people understand. There is a lot more to being an accurate shot, but these are the fundamentals, and if you can't achieve these you're accuracy will never be as good as it could be.
I'd also like to touch on different rounds and their effects.
5.56mm (.223)
This is a standard hunting and NATO military round in North America. It is a smaller, lighter round that flies fast and has a good dose of penetration. These rounds in a AR (assault rifle) platform are accurate to 300 or 400 meters, and effective to approximately 600. The difference is that while a round at 600 may not hit the target, it will still kill them.
7.62mm (.308)
This is the larger hunting / NATO military round, and one of my favourites. These rounds have a flatter trajectory and a heavier bullet, meaning they're far more lethal than the 5.56. These rounds are also heavier. I've used these to engage targets accurately at 500m - 600m, and ranged them out as far as 1400m in a mounted system in 40 round bursts with fairly good accuracy. These rounds will pound through brick, concrete, and plenty more, a sofa isn't going to stop these if you're going for the realism punch.
9mm
A very common pistol round, I don't know too much about these. I've only taken a 9mm pistol out to about 50 feet, and I found it fairly inaccurate. Admittedly I wasn't taking it all too seriously so the fault on that is likely on me more than the pistol. Typically though these rounds are used in conjuncture with a short barrel and so are inaccurate. If you used this size round with an extended casing in a rifle I might be worried, but as far as a pistol platform goes, I would acknowledge it as lethal, albeit limited in range.
12.5mm (.50 Cal)
A lot of people seem to think this is a super cool sniper bullet. I'm not saying it isn't. I will however state that
LAV's can be killed with them. These rounds are very capable and arguably the upper limit of what the military refers to as small arms. These will punch through concrete, metal, rocks, the earth, and damn near anything they want to unless it's been designed to stop ballistic weapons. These are effective even out beyond 1500m in some cases as soldiers have been documented killing people from those distances with them. Luckily this is set back by the rifles being heavy, and the rounds kicking like an angry horse.[/hr]