When an effect targets, it chooses at the time of activation the specific card(s) that it will affect.
You must declare the target before players are allowed to chain to the effect. If another effect is chained to the original effect so that the target is not a legal target when resolving the original effect, then you do not get to "re-select" the target. The original effect resolves without effect (that is, it does nothing).
- Example: Player A activates "Offerings to the Doomed" and targets "Dark Magician". Player B chains "Book of Moon", targeting the same "Dark Magician". "Book of Moon" resolves first, and changes "Dark Magician" to face-down Defense Position. Then, when "Offerings to the Doomed" resolves, "Dark Magician" is not destroyed - "Offerings to the Doomed" can only target face-up monsters, and "Dark Magician" is face-down, so "Offerings to the Doomed" resolves without effect. You do not get to select a new monster to destroy.
- Example: Player A attacks with "The Tricky". Player B activates "Draining Shield", which targets because it selects "The Tricky's" attack to negate. If Player A activates "Trap Jammer", then "Draining Shield" resolves without effect.
- Example: Player A activates "Monster Reborn" and targets "Blue Eyes White Dragon" in his Graveyard. Player B chains the effect of "D.D. Crow" from his hand, targeting "Blue Eyes White Dragon". Since "Blue Eyes White Dragon" is removed from the Graveyard, "Monster Reborn" resolves without effect.
- Example: Player A activates "Monster Reborn" and targets "Red Eyes Black Dragon" in Player B's Graveyard. Player B activates "Call of the Haunted" and targets "Red Eyes Black Dragon" in his Graveyard. "Red Eyes Black Dragon" is Special Summoned on Player B's field. "Monster Reborn" resolves without effect.
Cards like "Dark Hole", "Mirror Force", "Lightning Vortex" and "Raigeki" do not target, because the player does not specify which cards will be affected - rather, it destroys all monsters, regardless of whether or not the monsters were on the field at activation. Likewise, "Fissure" and "Magical Dimension" do not target, because they select the monster to be destroyed when you are resolving the effect.
Effects that automatically choose what they are going to affect, like "Drillroid" usually do not target. There are exceptions, however: "Sakuretsu Armor" and "Dimensional Prison" do target, but without input from the player. Most Counter Trap Cards do not target for the same reason - most can only affect the effect directly beneath it in the Chain, so there is no selection, so the effect does not target.
If the card's text says "target", then the effect almost always targets. If the card's text says "select", or "designate" then the effect usually targets, although there are some exceptions. When in doubt, check the card's rulings to see whether or not it targets.
An important thing to note is that Spell/Trap cards cannot target themselves.
- Example: Where this usually comes up is a player trying to get rid of a "Mystical Space Typhoon", so they can drop "Gorz the Emissary of Darkness", but the opponent not playing any Spell/Trap cards, or a player trying to use "Icarus Attack" when there aren’t enough cards on the field