Image from The New Solar System, Beatty & Chaikin.
Convection is the process responsible for weather on Jupiter, just as it is for the Earth's atmosphere. Gases from below rise, cool, and condense to form clouds. Jupiter's atmosphere has three kinds of clouds:
Image from The New Solar System, Beatty & Chaikin.
The temperature profile of each giant planet (shown above) dictates where the clouds will form - different molecules condense at different temperatures. Saturn contains the same cloud layers as Jupiter, but they are more spread out due to Saturn's lower gravity. Uranus and Neptune are cold enough to form methane clouds in their tropospheres. Methane absorbs red light and reflects blue light, hence the bluish appearance of Uranus and Neptune.
Jupiter and Saturn are probably colored reddish/brownish/yellow due to the interaction of sunlight and the gases in the atmosphere - it creates a "smoggy" compound (like what sits over Los Angeles or Juarez). However, the detailed nature of the colors is still not very well understood!
One of the important results from the Galileo probe, which entered Jupiter's atmosphere, is that the clouds thickness varies. This can also be seen in an infrared image of Jupiter, which shows thermal radiation (heat) escaping from portions of the atmosphere that have less cloud cover.
Image taken with the Hubble Space Telescope.
Image from http://www2.jpl.nasa.gov/sl9/image385.html.
Image from http://spaceprojects.arc.nasa.gov/Space_Projects/galileo_probe/htmls/IR_and_HST.html.
The giant planets all have VERY FAST east-west winds (200 m/s, or 450 mph!). The cause of the alternating jets is not well-understood, but it is likely related to the rapid rotation of the giant planets. Large storms also exist on these large planets: for example, Jupiter's Great Red Spot and Neptune's Great Dark Spot. Jupiter's Great Red Spot is a vortex (like a cyclone) that is maintained by Jupiter's high east-west winds. Why don't hurricanes last for hundreds of years on Earth?
