The initial instinct is to call the Sideboard fifteen cards situationally useful. A CoP: Green is situationally useful when facing a deck with mostly green sources of damage but is useless in other situations. So the first question is why use situationally useful cards at all? If you could put fifteen maximally useful cards into the sideboard, why wouldn't you?
The color-specific sideboard cards must do one thing: shut down that color completely. It becomes necessary to consider each card, if many are available, to see how it would affect the target color. Freyalise's Charm is a poor color-specific sideboard card in many ways because it does nothing to shut down a black deck's operation; Lifeforce is better, but its "shut down" ability is limited by the amount of green mana untapped at all times. A CoP:Black will shut down almost all black damage sources, but will not prevent a black deck from casting its spells. Karma does nothing to "shut down" a color, but it can be devastating to a heavy-black deck. The analysis, as can be seen by this example, should center around what the strength of the opposing color is -- then to attack it.
Color-specific sideboarding is often used as part of a more complicated sideboarding strategy, and only very rarely is it the primary sideboarding strategy among better decks.
This is generally the next level in theoretical complexity. The idea is to counter a type of strategy which poses a threat. For example, one might have 4 Guerilla Tactics in the sideboard for the Discard decks, or Pyroclasm for the weenie decks.
The complexity begins when one encounters a complex opponent. Suppose one wants to build a sideboard that combats a multi-prong offense deck based around red direct damage, creatures that are difficult to deal with, and white removal (Disenchants, Plows, Wraths, etc.). One might consider the Kim school as one example of such a multi-prong offense deck.
What do you do? A CoP:Red may not work as well since the opponent has targeted enchantment removal; plus, it has plenty of non-red sources of damage. A color-specific sideboard would fare poorly in this scenario. Simply putting in anti-creature cards may also prove to be a poor decision, depending on the card, since the Kim strategy means more than simply direct damage.
I believe that the successful strategy-specific sideboards are those which identify the vulnerabilities in a particular strategy and build a sideboard to exploit those vulnerabilities. Against a complex multi-strategy deck, it means choosing something which can affect as many of them as possible, but if not, the most important one. Obviously, being able to identify weaknesses and exploit them is an acquired skill which puts some players into the finals while the others go home early.
But for example, against a prototype Kim deck, the vulnerability of all of its strategies is that they are all fairly mana-intensive. The Blinking Spirit requires a great deal of mana to be able to "bounce" for protection. The Autumn Willow is GG4, the Mishra's Factory requires mana to attack, Fireballs take up mana, etc. The sideboard cards that one might look at, therefore, may be Armageddon, Infernal Darkness, Strip Mines, Winter Orbs, etc. Obviously, some decks cannot use these sideboard cards, but this is in the way of an example.
Strategy-specific sideboarding requires an understanding of the strategies which you are attempting to defeat and their vulnerable points. It tends to be defensive and reactive, but does not have to be.
This theory is not often seen or used, but when successful, it can be quite deadly. The idea is to transform the deck completely through sideboarding. The new strategy now implemented via sideboarding often catches the opponent by surprise and unprepared.
The best example is from a game I played recently against an apparently creatureless R/W Millstone deck with tons of permanent-removal via Bolts, StP, Disenchants, Pyroclasm, Wrath of God, etc. In the second game, I sideboarded out most of my anti-creature cards for more anti-artifact and anti-blaster cards. Suddenly, I see Orders of Leitbur, Uthden Trolls, Serra Angels, Shivan Dragons, etc. and no Millstone and no direct damage of any kind. My Disenchants sat in my hand as I was being pummeled by two Orders of Leitbur. Needless to say, that game was a lost-cause.
It turned out that the sideboard was composed almost entirely of creatures: 4 Orders, 4 Uthden Trolls, 2 Serras, 2 Shivans, and 3 Divine Offerings. By transforming the deck from one strategy to a whole new one, the deck won an easy victory.
The problem is that this type of sideboarding is a bit risky. Few decks are designed to perform as well in two forms. Even a slight inefficiency can cost a deck in a close game, so it becomes necessary to test the deck in all of its forms. Plus, if the opponent does not play a reactive sideboarding strategy transforming his own deck into something which cannot handle yours, then you may have lost the edge. Nonetheless, transformative sideboards are worth examining, depending on the main deck which you are running.
This is often combined with Strategy-specific sideboarding principles but color-specific sideboarding is also popular. The difference is subtle, but useful to contemplate. The idea is not to try and "hose" a color or a strategy but merely to enhance one's own main strategy's ability to handle them.
For example, an Energy Flux hoses a heavy artifact deck, whereas a Divine Offering merely enhances the ability to deal with such a deck. Obviously, the comparison is difficult to make and most people would not pick the Energy Flux because of their own artifacts. A strong case might be made, however, that depending on the deck, the Energy Flux belongs in the main deck and the Divine Offering belongs in the sideboard to "enhance" the anti-artifact strategy.
The key difference seems to be for predominantly defensive decks whose entire purpose is to take on all-comers, e.g. Weissman deck. Such decks have the option of attempting to hose a strategy or a color, but sometimes such hoser strategies can either backfire or make the deck less efficient. For example, the Weissman deck could put in Blood Moon against a Kim deck. That would hose the Kim strategy as much as it can be hosed. However, it would also slow down the Weissman strategy. What _may_ happen instead is that instead of Blood Moon, the Weissman deck may put in a couple of Divine Offerings for plowshares, reasoning that Jade Statues can be taken care of along with all other artifacts. Such a sideboard would be an enhancement sideboard, rather than a "hoser" sideboard.
Enhancement sideboards seem to be more popular among experienced players who are not comfortable with changing the basic character of their main deck with massive sideboarding. The idea seems to be that the basic strategy works and works well, so why change it completely? Instead, merely enhance parts of the basic strategy to plug holes or counteract the opponent strategy better. I personally do not yet grasp fully the complexity of this form of sideboarding and I believe it takes quite a bit of experience to approach the sideboard with this more flexible view.
As a way of experimentation, however, and this applies with special force in the Type II arena, I looked at how my basic strategy (U/W Weissman/Maysonet clone, listed below) handles the opposition. In Type I, it is possible to have a dominant deck that really does not require much sideboarding -- substituting plowshares for Divine Offerings merely strengthens the ability of the deck to handle an opponent creatureless deck -- but the basic operation (e.g., Mana Drain -- Amnesia -- Sceptre Lock) remains the same. In Type II, however, the scheme seems to be much more of a question of rock-paper-scissors. Mono-black Necropotence decks usually run over U/W defensive decks which usually beat R/G Ernham & Burn'em decks which usually beat the mono-black Necropotence decks. As a result, my sideboard ignores burn decks completely. It has nine cards against mono-black Necropotence decks, and four cards against other U/W defensive decks. The other two cards are general enhancement cards: Control Magic, and a Power Sink (arguably countermagic is the most "enhancing" of any defensive strategy as it hoses nothing but enhances everything).
In other words, I am using a color-specific sideboard strategy (Karmas, White Knights, etc.) in order to enhance my deck's ability to deal with a particular style of play: fast attack Necropotence decks. I attempt to "hose" black because there is no other way for my deck to deal with it. Contrast this subsection, however, with my approach to other U/W decks -- 2 Divine Offerings, 2 Disrupting Sceptres. My intent is simply to replace the useless cards (such as Wrath of God) with useful cards -- i.e., enhancement. It is not a strategy-specific sideboard. I would use Winter Orbs if I were attempting to "hose" the U/W defensive strategy. Yet, since that would change the character of my own deck substantially, I choose merely to enhance my ability to deal with U/W rather than try to hose it. The difference, again, may be too fine but I believe it exists and that the expert players take advantage of it in ways that less experienced players should attempt to learn.
Note: The above attempts to cover the principles regarding the _construction_ of sideboards. They obviously extend to making those decisions as well. However, deciding which cards to switch out and which cards to switch in is an important skill in and of itself. That skill, unfortunately, cannot be adequately described in a written document -- at least, I can't do it. If you have suggestions, please email them to me at rsh9395@is.nyu.edu.