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 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 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.

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.