Daytime Astrophotography
The sun is the main subject of daytime astrophotography activities, and the rare occasion of a partial or full eclipse is the ideal time to make a noteworthy picture of a celestial event during the daytime.
The Afterglow
Sometimes with a good light-sensitive camera (many of the new digital cameras fall under this category), an intriguing picture can be made after sunset, where the moon or perhaps Venus and a few stars can be captured along the horizon with a hand-held camera.
Tripods
A tripod will greatly increase one's ability to make pictures of celestial objects at night. Besides a tripod, you will need a camera with a B setting and a cable-release device so you can hold the lens open for as long as possible without shaking the camera.
The Milky Way
The Milky Way makes for a great subject matter on a warm summer night with no moon and the sky is ablaze with the myriad of stars. You can even include a silhouette of a person or some of the surrounding landforms. Be sure to keep the exposure relatively short (under a few minutes) so the stars don't move around.
Star Trails
To see how stars move at night, leave the lens open for several hours. You will have to stop the lens down and add some neutral density filters, but the results are fascinating.