A lunar eclipse starts everything off Friday night. The moon will pass into Earth's outer shadow, or penumbra. The moon won't be blacked out like in a full eclipse. Only part of the moon will be shaded, but it should be easily visible from much of the world.
Comet 45P, meanwhile, will zoom past Earth early Saturday morning. It will be an extremely close encounter as these things go, passing within 7.7 million miles of Earth. The comet, glowing green, will be visible in the constellation Hercules. Binoculars and telescopes will help in the search.