How many times do I have to kill a player before I am dominating them?
I've observed that sometimes I just have to make two kills in order to dominate a certain player, sometimes thrice or is there any other factor that matters?
This will be helpful to unlock certain achievements that depend on dominations.
You have to get any combination of four kills or assists on an opponent in a row (that is, without them getting either a kill or an assist on you) to dominate an opponent.
Once dominated, either a single kill or assist is enough to get revenge.
Check the TF2 wiki for more info on dominations.