Bloodthirst is a keyword ability.
Bloodthirst is an old mechanic, and hasn't shown up until 2012 Core Set. Bloodthirst is an ability with different scales.
"Bloodthirst X: If an opponent was dealt damage this turn, this creature comes into play with X +1/+1 counters."
If you have a creature with bloodthirst 3, then that means that when it comes into play, if your opponent was dealt damage whether by creatures or spells, it gets the counters.
There are two common ways to trigger Bloodthirst:
- Use Burn Spells like Lightning Bolt or Lava Axe to damage your opponent directly during the first or second Main Phase, then summon creatures with Bloodthirst during your turn after the burn spells are cast.
- Wait until after the Combat Phase of your turn, then if you assigned damage to your opponent directly with any of your creatures, summon those creatures with Bloodthirst during your second main phase (After your creatures assign damage and before you pass your turn over.)
- 702.53a Bloodthirst is a static ability. “Bloodthirst N” means “If an opponent was dealt damage this turn, this permanent enters the battlefield with N +1/+1 counters on it.”
- 702.53b “Bloodthirst X” is a special form of bloodthirst. “Bloodthirst X” means “This permanent enters the battlefield with X +1/+1 counters on it, where X is the total damage your opponents have been dealt this turn.”
- 702.53c If an object has multiple instances of bloodthirst, each applies separately.