What helps me smooth out when I am spinning fast is not focusing on pushing down or pulling up. I actually focus more on "scraping" at the bottom of my stroke and pushing over the top. The up and down part of the pedal stroke seem to work themselves out when you do it that way.

Unfortunately good spinning is just one of those things you have to do until you get good. I recommend flat ground with a gear you can spin, or small hills to start with. You want to be in control, not just hanging on for the ride.