In the last 18 years, we've had four dogs die, and two cats. Three of the dogs died of old age, one from liver cancer. One of the cats died from brain damage (she was abused by some kids at a schoolyard) about two years after we rescued her. The other cat that died, some dude was walking his pit bull through the neighborhood, and sic'd his dog on our sweet, gentle, trusting cat. (If I ever find out who that guy was, I have a baseball bat for him, but he's not been seen in our neighborhood since then.)

Sorry to say, there's no 'easy way' to get over it, if you were close to a pet that died. Mourning is a process, and you just have to go through it.