You can change the scale of the Star Map to give yourself a better view of the whole galaxy, or to look closely at some specific section of it. To do this, just choose " Zoom in " or " Zoom out " from the " Window " menu. Their command keys are Command-minus and Command-equal, respectively. A lot of detail is lost when you zoom out all the way.
Generally, you'll want to zoom out to get an idea of where you live, and then zoom in so you can tell what's going on. As the game progresses, you'll probably find that your neighborhood doesn't fit in your Star Map any more, so you'll want to use the middle magnifications.
You can click on the name of a star in the Budget Window to scroll the Star Map to that star and select it. When you select a star in the Star Map, the Star list will scroll to the current star and select it there.
The map window supports contextual menus; right clicking on planets and stars will give you current actions associated with each.