1) Get a trigger job. A good custom trigger job will be well worth the cost. Generally about a 2lb. trigger pull suits most applications. Any less and you might have some problems with the gun going off before you are ready, and more will cause you to pull too hard, thereby reducing accuracy.
2) Spend your money on a good scope & mounts. So often people will buy an awesome rifle and then buy the cheapest scope that they can find. They then spend a lot of energy and time wondering why the gun is not consistent. Buy a good quality scope (such as the Leupold). Also, spend the extra money getting solid steel rings and mounts.
3) Practice, Practice, Practice. Spend a lot of time shooting your rifle. You will become more familiar with your shooting tendencies, trigger break point, and expected results. That confidence will surely pay off when it counts.
Other things to consider are
AMMUNITION: What are you feeding your rifle? If the answer is cheap ammo such as Russian surplus then dont expect much. Buy good quality ammo. That should shrink your groups considerably. Since every rifle is different, one ammunition type work better in one rifle than in another, and different munitions will strike a target in different areas while the aim point is consistent. Have some fun and buy several different types of ammunition and consistency test them. Fire five to ten shots at a fresh target with different ammo types while aiming at the bull every time. For this test, hitting the bull isn't as important as tight groups, so keep your aim point consistent and line up with the bull every time. A load that groups nicely is revealed, then adjust the sights or scope to zero the rifle with your favorite ammunition type.
FOULING: Every time a bullet travels down the barrel, all kinds of junk is left behind. Over time, copper deposits from the jackets of the bullets will build up and decimate accuracy. I've seen people pull out their hair over a rifle because of this problem which is easily prevented and corrected. This is a good thing to check even if your rifle is shooting well. So we think we know how to clean a barrel, huh? Well, maybe we do, but lets test ourselves. I failed this test the first time I tried it. First, we need a rifle who's barrel has been allegedly cleaned since last fired. Now get a barrel mop or put a few patches on your cleaning rod and douse it with the copper solvent commonly found at firearm retailers. I mean get it soaking. Now lay the barrel on it's side and run the patch down the barrel one time leaving plenty of solvent behind. Wait five to ten minutes, then take a solvent laden barrel brush and run it down a few times. Now run a clean patch down the barrel and see what comes out. If the patch is simply the same color as the chemicals we left in the barrel, you have a very clean barrel. If the patch comes out blue or green, my friend, your barrel is copper fouled. Repeat this process until the patches come out clean. The soak and wait method works beautifully with regular powder solvent cleaning as well. Before my friend showed me this trick, I thought I knew how to clean a barrel.
STOCK: Are you using the original wooden surplus stock? If so, adding pretty much any replacement synthetic stock should improve accuracy. Many of the wooden stocks are either worn out or misshapen from years of moisture, abuse, or the victim of wood compression from improper storage techniques. The synthetics have many other side benefits, such as the added length, that may in and of themselves lend to a more steady firing position. A more extreme approach would be to bed the stock. Bedding is simply a way of adding epoxy or resin to the inside of a wooden stock so the barrel and receiver rest in a perfect mold of itself. If done right, this provides the absolute best rock solid foundation for a rifle to rest in but make sure you know what you are doing. Epoxy metal composites make great bedding compounds. You can use vasolene or glad wrap between the action and the barrel as a release agent.
CROWN: The very end of the muzzle on the barrel is called the crown. This should be smooth, rounded, and free of dings and burrs. This is the very last piece of metal the bullet contacts before it's free of the barrel. If there is anything present to snag the bullet or any metal missing to unevenly vent gasses then the rifle should be re-crowned by a qualified gunsmith.
