Let's say I cast two Healing Salves on a creature. Each would prevent the next 3 damage that would be dealt to that creature. Does this effectively prevent the next 6 damage that would be dealt? Or do they both try to prevent the same 3 points of damage?
You would prevent the next 6 damage that would be dealt.
How this works is you have an event that deals at least 6 damage, and two prevention effects that both want to prevent 3 damage. First when applying the damage event you look and see you have the two prevention effects trying to modify how much damage is dealt. You would then choose one of them to apply, and do the check for prevention effects again. You see there is still a prevention effect that can apply to the damage event, so you also apply that one. If all the damage hasn't been prevented yet it would go through the check again, find no prevention effect, and deal any remaining damage to the creature/player.
616.1. If two or more replacement and/or prevention effects are attempting to modify the way an event affects an object or player, the affected object’s controller (or its owner if it has no controller) or the affected player chooses one to apply, following the steps listed below. If two or more players have to make these choices at the same time, choices are made in APNAP order (see rule 101.4).
616.1a-d [These determine the order that the prevention effects take place, but since these both have the same precedence they don't matter in this case]
616.1e Once the chosen effect has been applied, this process is repeated (taking into account only replacement or prevention effects that would now be applicable) until there are no more left to apply.
It effectively prevents the next 6 damage.
Rule 616.1e says:
Once the chosen effect has been applied, this process is repeated (taking into account only replacement or prevention effects that would now be applicable) until there are no more left to apply.
If the first 3 damage has already been prevented, the second prevent doesn't need to do anything until more damage comes in.