Cost

Costs are paid before the activation of a card, not after. Cnd destroys "Seven Tools of the Bandit". fuck meBold textThere is no refund of Life Points because they have already been paid.
 * Step 2 doesn't resolve because the Trap Card was negated. There is no refund of Life Points. The Life Points were paid already. You don't get them back.
 * Step 1 resolves: "Mirror Force" resolves its effect.

Example #4: Chaining "Mask of Restrict" to "Cannon Soldier's" effect

 * Step 1: Player A Tributes a monster and activates his "Cannon Soldier's" effect during his Main Phase 2.
 * Step 2: Player B activates "Mask of Restrict" as a chain to "Cannon Soldier's" effect.
 * Step 2 resolves: "Mask of Restrict" is in play and prevents Tributing of monsters.
 * Step 1 resolves: The monster was already Tributed before "Mask of Restrict" was successfully resolved. Therefore "Cannon Soldier's" effect resolves and Player B loses 500 Life Points. However, now that "Mask of Restrict" is active, further Tributes cannot take place.

More Info for new players
Costs don't always have to be in Life Points. Monsters can be Tributed, cards can be discarded from the hand, etc.

In the lore of a card whose effect requires a cost, the cost description is separated from the effect description by a comma, a period or the word to.

Costs as a Discard
Cards like "Dark Core" and "Lightning Vortex" have a discard cost of 1 card from your hand.

Costs as a Summoning Requirement
Cards like "Chaos Sorcerer" require you to remove 1 LIGHT and 1 DARK monster from play from your Graveyard.

You cannot use a card like "Disappear" to remove one of those monsters from play before it's removed for the Summoning, or a card to remove a card from your opponent's hand before he/she does, because you cannot activate cards during a summon attempt.

Other Costs
Other costs include: discarding from the Deck or removing a monster(s) from play. Sometimes, though it is not stated, the positive effect of a card can be a cost in itself, such as with "Astral Barrier".

You cannot partially pay a cost. For example, if you're forced to discard 2 cards, you must discard 2 cards, unless another card effect bypasses this, or it is otherwise impossible to do so, such as when you have one or less cards in your hand. In the latter case, you would not be able to pay the cost, since it has to be paid in full upon activation. A cost is similar to a Compulsory effect. There are very few cards that can negate costs (for example, "Spell Economics").

A Maintenance Cost is a (mostly optional) cost required to keep a card on the field. Monster Cards, Spell Cards, and Trap Cards can possess a Maintenance Cost. These costs are typically paid during a player's Standby Phase, although there are exceptions to this. See Maintenance Cost for more details.

Misconceptions
Some cards' effects can lead players to believe they are paying a cost for activation when, in reality, they are not.

Here are some specific examples:

Example #1: Negation of "Two-Pronged Attack"

 * Step 1: Player A activates "Two-Pronged Attack".
 * Step 2: Player B negates "Two-Pronged Attack" with "Seven Tools of the Bandit"

Because destroying 2 of your own monsters is part of the entire effect not separated by a comma or a period, it is not a cost and your monsters are not destroyed.

Example #2: Negation of "Future Fusion"

 * Step 1: Player A actives "Future Fusion".
 * Step 2: Player B negates "Future Fusion" with "Dark Bribe"

In this card's case, although it is separated by 2 commas, there is no indication or suggestion that sending cards from your Deck to your Graveyard is part of an activation cost or requirement for this card.

Unable to Pay a Cost
Costs must be "appropriately" paid in order to activate an effect. If there is a card or effect preventing a cost to happen, then the card cannot be activated.

Discarding/Sending to the Graveyard
If a card such as Macro Cosmos is on the field, then effects such as Gravekeeper's Commandant or Brionac, Dragon of the Ice Barrier cannot be activated if the card to be discarded to the Graveyard would be banished instead.

Returning to the Hand
If a card or effect cannot be returned to the hand, then that card cannot be activated. For example: Your opponent has played a Mind Control on your Stardust Dragon. Since Stardust Dragon cannot be returned to the hand, then your opponent cannot return Stardust to your Extra Deck to Special Summon Genex Ally Birdman because a card MUST be returned to the hand. This also holds true with other Synchro Monsters, Fusion Monsters, Xyz Monsters, and cards that would be banished when it would leave the field, such as Plaguespreader Zombie or Quillbolt Hedgehog that were Special Summoned through their respective effects.