What are the chances of seeing Halley's Comet this weekend? Zero?
Well, not really!
The Orionid Meteor Shower, which peaks this weekend (October 20-22), is actually the Earth passing through the debris left by Comet Halley. Bits of rock and ice will burn up as the Earth's atmosphere moves through the debris trail. What we call a meteor shower is actually the incineration of comet trash!
You don't need a telescope to see a meteor shower – just look up! The meteors will peak this weekend after midnight on Friday and Saturday night. Look up and to the southeast for the best view. This weekend is just a few days after New Moon, and it will not interfere with your view of the Orionids.
A green Orionid Meteor. Photo by Brocken Inaglory, Wikipedia