The Parts
Actual specifics of the internal parts vary from manufacturer to manufacturer, but these are the basics of most modern stacked tube blow-back semi-automatics.

How the Valve Works

The valve system is the heart of the blow-back semi-automatic. It hold gas in the valve chamber, and when opened by a strike of the hammer, releases gas in two directions simultaneously - upward into the bolt to propel the ball, and rearward to blow the linked bolt and hammer back into a cocked position.  In most two-tube blow-backs, the gas directed toward re-cocking travels across a flat cut-out on the valve pin, however, some models such as the Diamond GT, have an extra hole in the front of the valve which allows dispersal of the re-cock gas.
 

How the system Works

Cocked Gun
Blow-backs fire from an open-bolt position, where the bolt is in an "open" position, with a ball in the breech, before the trigger is pulled. When the gun is initially charged up, the linked bolt and hammer must be manually pulled to the rear of the gun, which compresses the main spring, cocking the gun. The bolt hammer combo, which is under pressure from the main spring, is held in place by the sear.
 
 
 
 

Forward Stroke
When the trigger is pulled, it lifts the front of the sear. As the sear pivots, the rear lowers, releasing the bolt/hammer combo, which is carried forward by the decompressing main spring. The bolt pushes the waiting ball into the bore of the barrel. The sear spring pulls the sear back and down (note the sear not only pivots, but also moves back and forth).
 
 
 
 
 

Valve Action
As the hammer comes forward striking the valve pin, the pin moves the connected cup seal away from the valve, allowing gas (blue) to flow into the valve. The gas moves through the valve in two directions (blue arrows), both up and through the bolt to impact the ball, and back to impact the hammer, blowing the linked bolt/hammer combo back toward the rear of the gun (see closer detail on the valve above.)
 
 
 

Rearward Stroke
As the bolt/hammer combo travels back, it compresses the main spring, and travels across the sear. Meanwhile the next ball in the feed tube drops into the breech. Traveling rearward, the bolt/hammer combo impacts the rubber bumper in the back of the gun, which saves the end cap from damage. The bolt/hammer combo then returns slightly forward and is caught by the sear, pushing the sear forward. Meanwhile when the user releases the trigger, it is returned to it's "at rest" position by the trigger spring. The gun is then ready to fire again.
 
 

A few notes about the above animation: For purposes of clarity, the animation runs substantially slower than an actual blow-back. Unrestricted by the sear, a two-tube blow-back can easily cycle in excess of 20 times in a single second.  The animation also features a trigger with a retractable, spring-loaded trigger latch, which allows the trigger to pass the sear smoothly as it returns to it's rested position. The retractable trigger latch appears on guns like Spyders and Piranhas, but is not a feature on all blow-backs.

Tuning
The most common way to adjust velocity of the paintballs fired by blow-back semi-autos is to control the tension of the main spring. This can be achieved in several ways. On modern blow-backs, a spring tension adjuster (a.k.a. velocity adjuster) is often located in the rear cap of the gun. It consist of a screw which moves the spring guide (located inside the rear of the main spring) back and forth, thus putting more or less tension on the main spring. With more tension, the hammer strikes the valve pin harder, releasing more gas and increasing paintball velocity. With less tension, the opposite occurs. If the adjustment range of the screw is not enough to achieve the desired velocity, changing the main spring may be necessary. Most modern blow-backs have aftermarket spring kits available, which include color-coded springs of varying tension. If no alternate springs are available, with the proper size shims, a ball bearing, or other objects, the tension on the main spring can be increased. On the other hand, tension can be decreased by cutting the main spring, but that should be considered a final option, since it is not reversible.

Valve spring adjustments can also effect velocity, however the valve spring is not as easily accessed as the main spring, since the gun must be de-gassed first. More tension on the valve spring means the valve closes quicker, and less gas is released, resulting in a lower velocity. Less tension on the valve spring will result in the valve staying open longer, more gas released, and a higher velocity. The options for adjustment include swapping springs, using shims, or cutting the spring. Because the area is under gas pressure, few blow-back guns have ever featured tension adjustment screws for the valve spring (although it was an option on the Line SI Promaster)

Far less common and not so easily accessed ways of controlling the velocity on blow-back semi-autos involve physically changing the valve system and other parts of the gun. For instance, the shape of the valve pin can help determine how much of the gas is used for propelling the ball, and how much is used for re-cocking the action, while the hole in the top of the valve can determine the volume of gas allowed to flow into the bolt to propel the ball. Early blow-back semi-autos actually had parts made to allow adjustments in these areas, but the concept contributed to the complexity of the gun and was abandoned in later blow-backs. In modern blow-backs, such adjustments are only for those who like to tinker.

One thing to keep in mind when tuning a blow-back is that the amount of gas being released by the valve also affects the ability of the gun to re-cock. If the volume and/or pressure of the gas being released is too low, the gun will not have enough gas to re-cock. This often results in the "dead" effect where the gun simply does not try to re-cock after firing a shot, or the "full auto" effect where the gun tries to re-cock, but cannot blow the bolt/hammer back far enough to catch the sear, causing the hammer/bolt to come forward again, strike the valve open, and repeat the process. These effects are especially pronounced when trying to use the gun to with inadequate pressure (cold weather Co2 operation, or a tank running out of gas). In most cases, getting the correct spring combination, or adequate tank pressure will address the problem.

Common Problems
From a standpoint of parts failure, the cup seal takes the honor of "most likely suspect" in two-tube blow-back semi-automatics. Cups seals are made of plastic or some other semi-soft material, and hold gas inside the valve chamber by sealing the valve. Cup seals can be damaged by debris in the gas system, or sometimes just wear out. They are generally inexpensive and replacing one is a fairly simple matter, however, often a cup seal can be repaired through cleaning. Leaking gas heard down the barrel is indicative of a faulty cup seal.

Another source of problems with blow-back semi-automatics is O-ring failure. Depending on the design of the gun, a blow-back can have in excess of a half of a dozen o-rings. Although the failure of any of the O-rings could possibly stop the gun dead in it's tracks, there are only a few which are critical to the operation of the system. O-rings such as the ones located on the bolt are meant to help seal the gas in as it passes from the valve through the bolt, but the gun will operate without them. However, if those o-rings break, they could leave enough debris to jam up the action. The O-ring on the front of the hammer is a little more important. It helps the hammer catch the gas from the valve directed for re-cocking. With enough gas pressure, some blow-backs will function without the hammer O-ring, but having the O-ring in place makes the process more efficient. The more critical O-rings are the two that seal the valve chamber. The O-ring on the valve itself which seals the chamber usually suffers damage only during the removal or installation of the valve. If it is damaged, the result can be gas leaking down the barrel, much like a faulty cup seal. The O-ring on the front cap must be in working order or the valve chamber will not be sealed, and gas will leak from around the cap.

Although any hard part on a two-tube blow-back can wear out after heavy use, it usually takes tens of thousands of rounds before that happens. Among the most common hard parts to wear out is the sear. If the rear edge of the sear is broken, chipped, or worn down, it may not catch the hammer as it returns to it's re-cocked position. This is usually evident upon inspection of the sear.

The Basics
The list of possible modifications to improve performance could go on for days. However, for most players, those modifications should be considered "wants" as opposed to "needs".  Right off the shelf, modern two-tube blow-backs offer decent performance at a decent price, and are easy to use in an effective manner. When well maintained, they are probably more reliable than any other system available in paintball, and easy to repair if they fail. Taken as a whole, blow-back semi-automatics probably offer the best value among all paintball guns.