There is a state between them standing up and truly dead. They can be unconcious - bleeding to death or they can stabalise. If a character reaches -10 HP then they are dead, other they can be healed (either a character using the Heal skill, or salves/potions/spells of healing).
Just look out for writing that appears above their head saying whether they are losing hitpoints (like a countdown) or if they have stabilised. IIRC if they stabalise then the character will curl up into a ball rather than just lying there.
There are wands of Resurrection dotted around the game, but they are rare so avoid using those unless absolutely neccesary. Eventually your cleric will be able to raise your dead party members

.