At the risk of boring you all senseless
Lightning happens when electrons at the bottom of a cloud travel through the moist air (which acts as a conductor) to earth. They only travel at 60 miles per second which isn't that fast. They don't go straight down, but follow zigzag paths - there's speculation on why they do this (dust and impurities creating regions of air more conductive than other bits) but it's still not known. This group of travelling electrons is called a step leader, and has a purple glow. It's not the actual lightning strike - it's just laying down the road for the lightning to travel.
As the step leader gets near the earth, it repels electrons down into the Earth's surface. This makes the surface of the Earth even more positively charged. The positive charge (called a streamer) migrates upwards through anything above the Earth's surface - like trees and tall buildings.
It's when the stremer contacts the leader that the fun starts - then you've got a complete pathway for the lightning to travel and BANG the contact point between the positive and negative ions moves upwards at 50 000 miles per second. There are several surges - not just one, but they all look like the same one as it happens so fast. It's not the electrons you can see in the lightning strike, but the air: the immensely fast flow of charge between Earth and cloud heats the air around it and makes it expand. This is also the phenomenon behind thunder.
I don't know why lightning appears to go down - I would speculate that it's because most people expect it to be going down. At any rate, it moves so fast that I doubt the eye could detect movement at all. I don't know a definitive answer on this, but I hope the rest helps.