Define the process of "casting" a spell.

The process of "casting" a spell in Magic: The Gathering involves putting the spell onto the stack and paying its associated costs. This is a defined action within the game that initiates the spell's resolution process.

When a player casts a spell, they first announce it, then place it on the stack. After the spell is on the stack, the player must pay any mana costs or other additional costs required by the spell. This step is crucial because it reflects the game’s resource management and strategic play. Once the spell is cast, it remains on the stack until it resolves or is countered, and it can interact with other spells or abilities that may be on the stack at the same time.

The other processes listed do not accurately represent casting a spell. For instance, taking a card from the graveyard and putting it into play more closely resembles the action of bringing a permanent back into play rather than casting a spell. Similarly, exiling a card or placing it back in the library does not involve the necessary steps of placement on the stack and cost payment, which are essential to the act of casting. Therefore, the correct option captures the exact mechanics involved in casting a spell according to the game's rules.