This page is associated with the marker animations listing. This page explains the methods by which some generalized and some unique designs function in greater detail.
General Classification:
I classify markers into one of two main categories, and divide them up at that point into their respective models sub-categories and models. There are many different ways of classifying markers based on their general features. Personally, I believe the method on these pages to be largley effective (it goes without saying that I've spent considerable time pondering this concept). Please remember that there are many different designs and variations on designs that it simply becomes difficult to come up with a "perfect" classification, however as said I believe mine to be one of the best.
I drop all designs into one of two main categories, either markers with a hammer or markers without a hammer. This is done for the simple reason that all markers using a hammer/valve design will be essentially identical, except for how the parts are arranged and the non-specific support features (body shape, etc). All other markers that are hammer-less use their own respective designs, sometimes varying quite a bit from one-another.
Markers using a hammer
Markers without a hammer
Design Overlay: 
All markers have a resting state in which they will sit for the majority of time, until called upon to fire. When the marker fires, many things will happen, however the main action that takes place is a main push that will force the marker to fire the ball. This can be one of two things, either increasing force or decreasing force. The technical term for this action is a kinetic differential, which essentially means two opposing forces will push against one-another, and one is higher so it will overcome the other. The end result of this is called the derivative and is the state of the marker during the firing process.
Increasing force markers are much, much more common for a multitude of design reasons that are too lengthy to explore without describing how several markers work in massive detail (which is why I'm not going to bother right now). The basic action is that some type of force will be "released" when the marker fires, which will somehow allow the marker to release its pressurized air to propel the paintball. This is most often observed as the hammer in mechanical marker (described above in the "markers using a hammer" page).
Decreasing force markers are less common but not any less useful, they simply require different means to function. Again, without extensive explanation, the idle state of a decreasing-force marker is that something will "hold back" the pressure used to propel the paintball. When the marker moves to fire, this holding-back force is let go, which allows the pressurized air to fire the ball.
From a technical standpoint, a marker being increasing-force or decreasing-force is probably a better starting point for classification. However, the similarities between a hammer marker and another type of increasing-force design aren't always immediately apparent. Consequentially, I prefer to group the designs in other ways to help people visualize things.