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I saw these cards on the Internet and quickly became curious: How in the world do they work? Do you pick one of them to play and then discard the card, or can you play both? How does their color and mana-cost duality function with cards that depend on them? When were these cards added to MTG?
Note: The answers given here were correct at the time they were written, rules changes have since made parts of them incorrect.
They work as if they only had one of the sides attributes while on the Stack, and as if they had both sides' qualities in every other zone.
If an effect is asking for a particular characteristic, it gets two answers. For example, Infernal Genesis asks you to reveal the top card of your library and add a number of 1/1 tokens to the battlefield based on the converted mana cost of the revealed card, if you revealed Hit//Run you would get 8 tokens, because the converted mana cost of the card would have two answers 3 and 5.
If an effect is performing a comparison, it only gets one answer. If either side would return a Yes answer when performing the comparison, then you would get a single Yes. For example, if you used Sunforger to search your library for a card that was red or white and had a converted mana cost of 4 or less, you could search out Wax/Wane (because for one of the sides, you would get a yes - Wane is white, and has a CMC of 4 or less) and still cast the Green side (Wax) of the card (only the search is restricted by color and CMC).
When casting a split card, you choose a side and proceed to do the normal process for casting a spell. Announce the spell, choose targets, pay costs, etc.
The Split Card type was added to MtG first in Invasion Block.
708.2. In every zone except the stack, split cards have two sets of characteristics and two converted mana costs. As long as a split card is a spell on the stack, only the characteristics of the half being cast exist. The other half’s characteristics are treated as though they didn’t exist.
708.2a If a player casts a split card, that player chooses which half of that split card he or she is casting before putting it onto the stack. Only the half that is being cast is considered to be put onto the stack.
As of Amonkhet, these cards no longer give separate answers for characteristics - they give one answer that combines the characteristics of both halves. Some of this makes no difference, as explained here Infernal Genesis will still give 8 tokens for Hit//Run because it now gets one answer, 8, instead of two answers 3 and 5. Other times the difference matters, Isochron Scepter can no longer imprint Bound // Determined because the card no longer returns 5 and 2 for CMC, it returns just 7.
There are now different kinds of cards split similar to these, and some of the rules have changed since the original question was asked.
For example: Fire // Ice. These cards are read with an “and” joining the two names, thus “Fire and Ice”.
These cards work exactly the way you asked, you cast one half of the card for the casting cost, get that effect and the whole card goes to the graveyard. You don't have the option to cast the other half.
Example: Turn // Burn. These follow the same naming pattern as basic split cards, thus “Turn and Burn”.
In Return to Ravnica block, a new ability was given to split cards, fuse, which allowed you to cast both halves. The cost would be the combined cost of both halves, they would be put on the stack as a single spell and would resolve starting with the left half (which usually made the right half work better anyways). You could chose to play only one half of the split spell.
For example: Never // Return. These cards are read with a “to” joining the two names, thus “Never to Return”.
In Amonkhet block, cards with another new ability, Aftermath were printed. These cards had the top half printed as a spell normally, with the bottom half turned sideways. You could only cast the top half normally, the bottom half would be cast like flashback, from the graveyard then exiled.
The rules for split cards changed, the most recent change was when Aftermath cards were created in Amonkhet. Before the cards would be seen as both separate and combined by effects letting Wear // Tear be seen as a 1, 2 and 3 CMC spell. This let some spells be abused by using the smaller half to meet the imprint requirements of Isochron Scepter but casting the higher half, or using Counterbalance to get three CMCs worth of counter power. Now the CMC of split cards is always the combined CMC of both halves, EXCEPT while the spell is being cast and on the stack, where only the parts paid for are counted. The same is true for the colors of the spell, the colors of a split card are both colors everywhere EXCEPT on the stack when being cast, where only the cast part(s) colors are used.
This is covered in the comprehensive rules:
708.4 In every zone except the stack, the characteristics of a split card are those of its two halves combined. This is a change from previous rules.
708.4a Each split card has two names. If an effect instructs a player to choose a card name and the player wants to choose a split card’s name, the player must choose one of those names and not both. An object has the chosen name if one of its names is the chosen name.
708.4b The mana cost of a split card is the combined mana costs of its two halves. A split card’s colors and converted mana cost are determined from its combined mana cost. Example: Assault/Battery’s mana cost is {3}{R}{G}. It’s a red and green card with a converted mana cost of 5. If you cast Assault, the resulting spell is a red spell with a converted mana cost of 1.
708.4c A split card has each card type specified on either of its halves and each ability in the text box of each half.
For example: Brazen Borrower
Adventure cards are not split cards, but are still two spells on one card. They have a main spell that is a creature, and an adventure spell that is an instant or sorcery. The text box shows the creature side on the right, and the adventure spell on the left.
You can cast either half as normal. If you cast the adventure spell, the card is exiled as it resolves and the creature half can be cast from exile. If you cast the creature half from hand, it resolves and you cannot cast the adventure spell.
These do not follow the split card rules listed above, since they are not split cards; instead they follow the Adventurer rules. Adventure cards are treated as if they are only the creature half at all times except when they are on the stack being cast as the adventure.
