After the mothership releases your landing module, use the left and right arrow keys to avoid the orbiting asteroids. While descending the up arrow can be used for extra thrust to slow decent to help squeeze through those tight spots.
Right before touch down on one of the landing pads make sure that the thrust is going for a gentle landing otherwise your ship will crash.
After landing the module picks up a passenger and automatically launches. Use the arrow keys to steer again, but this time you can shoot those pesky rocks. To Fire press SPACE. As you reach the top of the screen, steer exactly to the center of the mothership. If you line them up close enough the module will dock with the mothership.