Rest shrines are tall monoliths with a blue symbol found in quests and wilderness adventure areas that can be used to replenish hit points, spell points, and special abilities (like Turn Undead or item clickies) as well as remove negative ailments and reset the death penalty.
Resurrection shrines are tall monoliths with a red symbol found in quests and wilderness adventure areas that can be used when dead in order to resurrect with a tenth of one's maximum hit points and whatever spell points they had at the time of death. Note that you will suffer a temporary negative level due to the death penalty.
A dead player's Soul stone must be within 10 seconds of walking distance to the shrine in order to use it. Resurrection shrines can be used as often as needed.
In order to use a Resurrection Shrine with a hireling, you must be holding the Soul stone in your inventory, target the shrine, and then instruct the hireling to interact with your target. They will then be resurrected.