It travels DOWN to the ground - the myth that it goes upwards comes from the "streaming" which objects on the ground give off just before a strike. It looks like a tiny lightning stike headed skywards, and is followed by the groundstrike from the cloud, or to be accurate, groundstrikes, as once the charge has earthed, that "connection" is used many times in a split-second, as the cloud discharges.
Actually it's a bit of both. Lightning is caused by the large amount of nitrogen in the air along with static electricity literally caused by fast moving air and other particles in the sky. Electricity works by the attraction between negative and positive components. The negative component is more 'stretched' while the positive is 'comdensed'. The effect being a large bolt of negative electricity hiting a small amount of positive. Ie lightning travels towards the ground to the large extent but meets the positive coming up a few feet. Only and the join does any lightning occur.
There are lots of theories on how lightening is formed, why it travels from ground to cloud sometimes and why it travels from cloud to cloud...why it takes the path it does. There is evidence that after the initial strike, that there is also a return strike. Then there are those blue sprites and and....hmmm....forget what the other ones are called. Anyway, they are seen above the clouds. Check out nasa.gov for some interesting info on lightening & sprites.