The Sloan Digital Sky Survey (SDSS) has developed several labs for classroom and personal use. In class, we began exploring the scavenger hunt, which is a great way to familiarize oneself with the SDSS tools. There are several more advanced labs available, as well as some very simple ones for kids which involve making sketches and interpreting drawings.
The Universe lab is also a good one to help get a grasp on the scale of things. It includes making a model universe with a balloon, and a discussion about how astronomers measure distances.
The most exciting phrase to hear in science, the one that heralds new discoveries, isn't 'Eureka!' but rather 'hmm....that's funny.' -- Isaac Asimov
The goal of science is to understand the world around us. In most sciences, one performs controlled experiments to help understand the thing being studied. In astronomy, since we are dealing with the whole universe, we cannot perform direct experiments on most of our subjects. But the basic method for exploring our questions about the universe is the same across all branches of science. Keep in mind, however, that the list below is merely a guideline: sometimes the question comes first, which leads to the observation. Sometimes a model is developed to explain one thing, which prompts questions about something else.
This is not the end of the process, by any means. The inital hypothesis rarely matches what is subsequently observed. Science is a dynamic process: scientists are constantly asking new questions, and new observations are requiring changes to old hypotheses. Less that 100 years ago, we did not have any idea what made stars shine. It required many developments in nuclear physics in the 1920s and 1930s before Hans Bethe came up with a hypothesis that matched our observations.
Notice that I have not yet used the word theory. A scientific theory is something that has survived many iterations of this process, and is the best explanation for the observed facts. This does not mean a theory cannot be revised! If new observations are not explicable by a given theory, some new hypothesis must be developed that explains not only the new observations, but all old observations where the previous theory was successful. Bethe's explanation for the shining of the sun is now a very well tested theory, but for many years, it made predictions that were not observed. In the end, his theory was right, but we needed to revise our understanding of fundamental nuclear processes! This was refered to as the Solar neutrino puzzle, and it was only solved in 2001!
For a more in depth discussion of the scientific method, and what constitudes scientific proof, I direct you to: Talk.Origins Archive: Scientific Proof?