Multiple instances of bloodthirst are cumulative. For example, if you control Bloodlord of Vaasgoth and cast a Vampire creature spell that already has bloodthirst 1, that Vampire will enter the battlefield with four +1/+1 counters on it if an opponent has been dealt damage that turn.

A creature spell like Phantasmal Image that may enter the battlefield as a copy of a creature is not a Vampire creature spell, even if you intend on copying a Vampire creature when that creature enters the battlefield.

Vampire creatures you put directly onto the battlefield without casting them and Vampire creature tokens you put onto the battlefield will not gain bloodthirst 3 from Bloodlord of Vaasgoth.