This article is strictly geared towards qualified, professional gunsmiths who are both accredited and insured and have sufficient experience to perform work on semi-automatic pistols. Also caveat: this article is more geared towards accurizing for "bullseye" or NRA conventional pistol than for IPSC, IDPA, USPSA, etc.
Accurizing the Beretta M9 (or 92FS, which is the model number given to the version that is available to the civilian population in general) is something that competitive shooters have been doing for a while now, but how to do it is a relatively unknown art.
Luckily, it is not that much different from what you would need to do to make just about any gun accurate. There are some options that can also make the gun last a lot longer if you are a competitive shooter and need the frame (made of aluminum) to last for 10,000 rounds or more.
The most difficult part of the whole process is the trigger job itself, which allows the shooter to fire the gun accurately without disturbing the sight alignment. Most military-grade guns "out of the box" have a relatively heavy "single action" trigger pull of between 5 and 8 pounds for safety reasons (i.e. to avoid accidentally discharging the gun). For many marksmanship competitions, trigger pull must be at least 2.5 to 3 pounds. For "Service Pistol" competitions, the rule is 4 pounds minimum. If you are not a professional gunsmith: take the gun to a gunsmith, let him/her handle that part of the work. You will be happier with the result for a variety of reasons, not the least of which is the fact that doing a trigger job on a Beretta is a major pain. It requires several iterations of taking the sear out of the frame and re-installing it to test pull weight, and getting the sear in and out of the gun is difficult even if you've done it a hundred times. So do yourself a favor and just tell your gunsmith what your minimum trigger pull needs to be.
If you are a professional, qualified and insured: the trigger pull weight on a Beretta results from a combination of the condition of the sear surface and hammer hook surface, plus spring condition.
Sear and hammer surfaces. The sear has a return spring which must be carefully removed and re-installed correctly whenever work is done on the sear. Take pictures prior to removal to ensure you can replace it the way it is supposed to be. The sear surface must be polished (buffing wheel or rotary tool) and a relief angle cut (similar to what you would do when doing sear work on a 1911) but do not modify the sear angle itself, or the gun could be unsafe. The hammer hooks need to be polished with a stone. Apply pressure-sensitive marking material (Dykem or other layout fluid), re-assemble everything and test everything. Disassemble and observe the bearing surfaces of the sear and hammer hooks to make sure there is consistent sear contact across the entire width of both the hammer hooks.
The springs involved are: the trigger return spring, the hammer spring (main spring), the sear return spring, and the firing pin blocker "lifter" plunger spring. Of all of these, the trigger return spring has the greatest effect, and the sear return spring has the least effect. You will likely see no effect from any change to the sear return spring, and modifying it may affect functionality. The hammer spring can be modified or changed out for a lighter (read: smaller wire diameter) spring from Wolff. The standard Beretta hammer spring is about 19 or 20 pounds. A heavier spring will give a higher trigger pull weight, and a lighter one will give a lighter trigger pull. The trigger return spring has the greatest effect on trigger pull. The stock trigger return spring is a round spring with two legs, and it eventually wears out, making the trigger too light. It also cannot be easily or reliably tuned, just replaced with another stock one. However, Wolff (http://www.gunsprings.com) makes a neat little unit that replaces this spring with a coil spring over a plunger. If you know what you are doing, it is possible to remove the coil spring and replace it with one of a different wire diameter (heavier or lighter) to tune the trigger pull. The blocker spring can be changed out, but this will only change the trigger pull in a very small way on most guns.
The Beretta does not have an over-travel adjustment as a stock option. Having an over-travel stop is a big deal for performance. So, you will need to purchase a steel trigger to replace the plastic one (costs about $15). Drill a hole in the trigger as high up as possible, tap it out for 6 x 32 tpi and install a set screw so that you have an adjustable over-travel stop.
To be accurate for bullseye pistol shooting, the barrel must be match grade. Bar-Sto and KKM Precision both make good barrels for the Beretta, and you can get very good results from just using a drop-in barrel. Contrary to common belief, there is no need to use a bushing at the front of the barrel to improve lock-up on a Beretta. The barrel locks up at the back against the slide using the locking block that is attached to the barrel, so it is imperative that your locking block is tight and in good condition. If you are installing a barrel that requires fitting, you will be removing material from the back of the barrel until the gun will go into battery reliably. Make sure and apply Dykem or other layout fluid between removing material to see where the contact points are. You want as much contact as possible between the back of the barrel and the breech face on the slide. Some barrels (Bar-Sto) have extra material on top of the back of the barrel and some of this must be removed slowly. The point of the extra material on these barrels is to get a tighter lockup with more contact surface, plus center the back of the barrel vertically on the breech face.
To improve lockup, some guns have set screws installed running up under the frame rails by the back of the barrel to give extra contact points while everything is locked in battery.
To improve service life, some gun builders modify the frame rails and replace sections of the aluminum rails with pieces of steel, affixed with screws. This is only necessary if you are a top level competitor and need that extra 2% performance that comes with a super tight frame-to-slide fit, plus the durability of steel on steel vs steel on aluminum. There are no "kits" for doing this type of work, so you will need to have this type of work done by someone who knows what they are doing. This type of improvement of slide-to-frame fit is similar in nature to the "Accu Rail" improvement that used to be done on 1911 style pistols.
Finally, sights. If you replace the rear sight with an over-sized adjustable sight, it is common to need to trim down the top of the firing pin blocker lifter to keep it from hitting the bottom of the sight. You will also need to get a taller front sight. The front sight can be welded on (less common) or you can get one that slips over the stock front sight and pins in place (more common) or you can get the slide milled out with a dovetail (uncommon). Beretta makes an adjustable rear sight that allows you to keep the stock front sight and not have to modify the blocker lifter, but it is more low-profile than most competitive shooters are going to want.