The effect "When your opponent's monster declares an attack: Toss a coin and call it. If you call it right, the attacking monster's ATK becomes 0 until the end of the Battle Phase" makes a Chain Link. (It does not target.)
When an opponent's monster declares an attack, if the card "Fairy Box" is activated, the effect "When your opponent's monster declares an attack: Toss a coin and call it. If you call it right, the attacking monster's ATK becomes 0 until the end of the Battle Phase" can be activated in the same Chain Link as the activation of the card.
"During each of your Standby Phases, pay 500 Life Points or destroy this card" is a maintenance cost to keep "Fairy Box" on the field. (It does not make a Chain Link.)
Previously Official Rulings
These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
If you have two copies of "Fairy Box" active on the field you may flip a coin twice, but only need to call 1 correctly to reduce the attacking monster's ATK to 0.
The current ATK is reduced to 0, including all Equip Spell Cards. Trap Cards and Quick-Play Spell Cards cannot further increase the monster's ATK this battle. A monster effect such as "Injection Fairy Lily" can increase its own ATK after "Fairy Box" is successful.
Paying 500 Life Points is optional, if you choose not to pay "Fairy Box" is destroyed.
The effect of "Fairy Box" does not target, so "Lord of D." will not prevent "Fairy Box" from reducing the ATK of an attacking Dragon-Type monster to 0.
Mentions in Other Rulings
Luminous Soldier: If the ATK of "Luminous Soldier" is reduced to 0 because of the effect of "Fairy Box" the ATK will increase by 500 points in the Damage Step if it is battling with a DARK monster.
Ordeal of a Traveler: When "Ordeal of a Traveler" & "Fairy Box" are both active, "Fairy Box" (mandatory) is step 1 of the chain, and "Ordeal of a Traveler" (optional) is step 2.
The Hunter with 7 Weapons: When you declare an attack with this card against a monster of the selected Type, and the opponent activates "Mirror Wall", the ATK will be halved first at attack declaration, and then increased by 1000 during damage calculation. So the final ATK will be 1500 = (1000/2) + 1000. Similarly, if the opponent activates the effect of "Fairy Box", the ATK of this card will become 1000, because the 1000 point increase occurs after its ATK is reduced to 0.
Waboku: SCENARIO 4: Player A's "Mega Thunderball" attacks Player B's "Mega Thunderball". Player B activates "Fairy Box" or "Mirror Wall". Player A activates "Waboku". RESULT: Player A's "Mega Thunderball" (with reduced ATK) is not destroyed, nor does Player A lose any life points, because of Player A's "Waboku". But because Player A's "Mega Thunderball" had reduced ATK, Player B's "Mega Thunderball" is not destroyed either.