That's a loaded question...to give you a detailed answer would take
several text-books on quantum mechanics, but to give you a sketchy
picture is pretty easy (so that's what I'll do):
we sometimes see of electrons making orderly circular orbits around a
nucleus (like little planets in a micro solar system) is clearly wrong,
nevertheless it helps picture part of what is going on. We know the
electron and the nucleus are attracted to each other by the
electromagnetic force, and are somehow "bound together" (just like the
earth and the moon are).
The thing that is a little harder to
visualize is the way the electron "orbits" the nucleus. The mathematics
of quantum mechanics, (which allows us to study atoms the same way that
Newton's F=ma allows us to study big objects), tells us that the
electron is more like a cloud that surrounds the nucleus. In other
words, the position of the electron is not at all well defined (like a
little planet) but rather it is smeared out over a large volume all
around the nucleus. Picture the nucleus as a tiny grain of sand that
lives at the middle of a puff of smoke, which is the electron.
shape of the electron "cloud" or "smoke" depends on how many other
electrons are caught by the nucleus, how much energy the electron has,
and other more subtle things as well. Sometimes the cloud will be
spherical, sometimes it will be shaped like a doughnut, sometimes like
a dumbbell etc.
If you look in a high-school chemistry book, or a college level modern-physics book you can find out more.
(republished on 07/21/06)