How do storms move across the earth?
With the prevailing winds.
Storms will move with the prevailing winds, west to east generally depending on the pressure pattern. If you look at the winds at the 500hPa pressure level (about 18,000ft) storms move in the same direction at approx. half the wind speed.
Tropical cyclones, however, are such intense lows that they don't really conform to pressure patterns, since they make their own. That is why it is somewhat harder to predict the track of a tropical cyclone.