Resurrection is the concept of a living being coming back to life after death.
Essentially, resurrection involves a goddess raising their hero from the dead so that they can carry on doing stupid things in their goddess's holy name. The method used varies, but usually involves a rusty defibrillator (possibly found in the guts of a dead monster, ironically deceased due to a myocardial infarction) and if the hero is lucky, their goddess will use powerful anesthetic to make the process less of an annoyance (i.e. lots and lots of beer).
More cautious goddesses tend to call an ambulance (or at least teleport it to the scene without even asking), but when all else fails, a goddess can always just let the dumb hero die and then go and make a deal with an anthropomorphic representation of death. The reaper of souls is bound by universal law to honor their contract, so no worries there then.
Death of a Hero
After a hero dies, all buttons on the remote control are temporarily replaced with just one option, 'Resurrection'. Resurrection costs 0% godpower to use and will instantly bring the hero back to life. If a god doesn't resurrect a hero for roughly 24 hours, the hero will resurrect himself, but they may be in a bad mood for quite a while afterward. It is recommended that gods resurrect heroes as soon as possible so as not to slow quest progress.
If one resurrects their hero/heroine within a few minutes of the hero/heroine's death, then they have a chance to receive some extra start-up gold.
Upon dying, the Magical Death Transportation Ferry gently carries the hero's lifeless body to the hero's most recently visited town. Accordingly, when a hero is resurrected, he will find himself in that town, usually in some sort of shrine.
Also, if a hero has an aura of reviving, he will automatically resurrect himself after just one minute. This is probably the most sure-fire way of making sure a hero isn't slowed down from something as insignificant as death.
Death of a Pet / Knocked Out Pet
Pets in Godville can't die since an update in 2012. They can only be knocked out and therefore don't need resurrecting. To see how to heal a pet consult the Pets page and Strategies for Pet Healing.