Advanced Gameplay FAQ: Chains, Activation, and Resolution.

A Chain is what happens when several card effects are trying to happen at the same time. By building a chain, you can more easily determine how the effects resolve.
Activation is when you declare an intent to use a card: flipping a Trap Card face-up, announcing that you are using a monster's effect, flipping a face-down Spell Card, and playing a Spell Card from your hand are all examples of activation.

Resolution is when you carry out the effects of a card.

When you chain multiple Spell/Trap Cards together, their activation (intent to use the card) is declared, one after the other. But no cards have resolution until nobody wishes to chain (activate) more Spell/Trap Cards.

A simple 2-card chain works like this:

Step 1 is activated (Spell Card played, Trap Card flipped face-up, etc.).
Step 2 is chained to Step 1 (activated).
(neither player wishes to chain additional cards) (resolve in reverse order)
Step 2 Resolves.
Step 1 Resolves.
In a 3-card chain:
Step 1 is activated.
Step 2 is activated.
Step 3 is activated.
(neither player wishes to chain additional cards) (resolve in reverse order)
Step 3 resolves.
Step 2 resolves.
Step 1 resolves.

Note on terminology: Some Continuous Trap Cards have effects that can be re-used, such as "Ultimate Offering", "Skull Lair", etc. To "activate" these Trap Cards is to flip the Trap Card from face-down to face-up, just like with any other Trap Card. Once the card is activated, you may "use" the card, or "use its effect", or "activate the effect." These are all synonymous terms but are different from activation of the card (which still means flipping the Trap Card face-up). The "use" of a Continuous Trap Card's effect (which has a Spell Speed of 2) can be chained and can be chained to. You CAN activate (flip face-up) a Continuous Trap Card and also use its effect in the same chain.

IMPORTANT: When resolving a chain, as the cards resolve they are NOT sent to the Graveyard until the entire chain has resolved, or a card specifically destroys them. This is important for cards such as "Princess of Tsurugi" and "Secret Barrel" where the effect depends on the number of Spell & Trap Cards on the field.

Example #1:
Step 1: Player A Flip Summons "Princess of Tsurugi."
Step 2: Player B chains "Barrel Behind the Door" to the effect.
Because "Barrel Behind the Door" remains on the field until the chain resolves, Player A takes 500 points of damage (1 Trap Card on the opponent's side of the field) from "Princess of Tsurugi's" Flip Effect.

Example #2:
Step 1: Player A Flip Summons "Princess of Tsurugi."
Step 2: Player B chains "Barrel Behind the Door" to the effect.
Step 3: Player A chains "Seven Tools of the Bandit" to "Barrel Behind the Door."
"Seven Tools of the Bandit" resolves first, and destroys "Barrel Behind the Door", which is sent to the Graveyard immediately. "Princess of Tsurugi" does zero damage to Player B because Player B has no Spell or Trap Cards remaining on the field since "Barrel Behind the Door" was destroyed and sent to the Graveyard.

Example #3:
Step 1: Player A activates "Secret Barrel."
Step 2: Player B chains "Ring of Destruction", her only card on the field or in her hand.
Even though "Ring of Destruction" resolves first, "Secret Barrel" still does 200 damage to Player B because "Ring of Destruction" is on the field when "Secret Barrel" resolves.