The stars are all about us, all the time. It is like the Earth is spinning around while being surrounded by a firmament of stars, the celestial sphere. Of course, we cannot always see all the stars. When then sun is out, the faint twinkling of stars is washed out. And the Sun changes its position with respect to the stars. The Earth revolves about the Sun (west-to-east); this yearly motion causes some stars to be seasonal. We can't see the stars of Taurus in the summer, since from our viewpoint on Earth, the Sun is in the way. Similarly, we can't see Sagittarius in the winter. From our perspective, as the Earth revolves around the Sun, the Sun appears to move through the celestial sphere, as it is projected in front of different stars. The path that the Sun follows is called the ecliptic. The constellations that the ecliptic passes through are called zodiac constellations. Because the rotation axis of the Earth is tilted with respect to the path the Earth takes around the Sun (by about 23.5 degrees), the Sun will sometimes be positioned in the northern sky, and sometimes by positioned in the southern sky. This causes seasons. On June 21, the northern summer solstice, the Sun is at its most northern position in the sky, 23.5 degrees above the celestial equator. This is when the North Pole of the Earth is tipped directly towards the Sun. Conversely, on Dec 21, the North Pole points directly away from the Sun, and the apparent position of the Sun is at its most southern point. This is the winter solstice. In between, on March 21 and September 23 are the vernal and autumnal equinoxes, when the Earth's axis is perpendicular to the line between the Earth and the Sun.
Note that one consequence of the Earth's revolution about the Sun is a confused definition of the word ``day''. It takes the Earth 23 hours and 56 minutes to rotate once with respect to the stars on the Celestial sphere. This is a sidereal (or star) day. But during this time, the Earth has moved a bit along its journey around the Sun. It therefore takes about 4 minutes longer for the Sun to return to the same position in the sky. We use this solar day. If we didn't, then in 6 months, we'd be eating lunch in the middle of the night! (And, because we use the solar day, the stars rise and set 4 minutes earlier each day.)
The final motion we have to consider is called precession. Think of the Earth as a top spinning in space. As mentioned above, the axis of this top is tiled by 23.5 degrees with respect to the path the top takes around the Sun. This causes the top to wobble. Although the tilt remains at 23.5 degrees with respect to the Sun, the direction of the Earth's axis slowly changes. Every 26,000 years the axis will complete one circle. What does this mean? Well, right now, the Earth's axis is pointed towards Polaris. But 13,000 years ago, it was pointed 47 degrees away from Polaris. Right now, the Earth's northern axis points towards the Sun when the Sun is in Gemini. So our summertime constellations include Sagitarrius, Scorpius, and Hercules. In 13,000 years, when the Sun is in Gemini, the Earth's northern axis will point away from the Sun. It'll be winter. This precession of the equinoxes is responsible for the difference between the Julian and Gregorian calendars, and why the year 2000 isn't a leap year. We want it to be warm in summertime! It is also why, when you read the horoscope column in the newspaper and it says that some planet or the Sun is in Gemini that it's not. It is in Taurus. Go take a look!
After the Sun, the Moon is the brightest object in the sky. Of course, the light we see doesn't originate on the Moon -- the Moon (like the planets) shines by reflected sunlight. [Note in passing: the Moon's surface is actually quite black. Only about 3% of the Sun's light which hits the Moon is reflected. But that's enough to light up our night sky.] The most prominent feature of the Moon's appearance in the sky is the Moon's phase. The Sun, of course, only lights up 1/2 the Moon -- the half that is facing the Sun. This doesn't always correspond to the half that faces the Earth. In fact, if the Moon is on the same side of the Earth as the Sun, we won't see the Moon at all. It's what we call a New Moon. If the Moon is on the opposite side of the Earth as the Sun, then we have a Full Moon, and we can see the entire 1/2 that the Sun lights up. Note that this means we can tell time by the Moon. We normally tell time by the Sun. For example, if the Sun is near the meridian, then it's around noon; if it's setting then its around 6 p.m. However, as you can see from the diagram, the phase of the Moon tells us the angle between the Sun and the Moon. We see the Moon and we know the angle to the Sun, so we therefore know where the Sun is. Hence we know the time.
The Moon makes one trip around the Earth (west-to-east) in a little over 27 days. But, once again, there is a difference between the one trip around with respect to the stars (the sidereal month), and one trip around with respect to the Sun (the synodic month). As we saw when considering the Sun, the synodic month (i.e., New Moon to New Moon) is longer, about 29 days.
The Moon does not orbit the Earth in quite the same plane as the Sun -- the circle it takes on the sky it tiled from the ecliptic by about 5 degrees. Hence the Moon spends 1/2 its time just slightly north of the ecliptic, and 1/2 its time slightly south of the ecliptic (but always in a zodiac constellation). Twice a month, the Moon's path crosses the ecliptic. If the Moon happens to cross the ecliptic at the exact spot the Sun is, the Moon will block out the Sun's light, and we'll have a solar eclipse. (This does not happen often. The Moon is rather small and casts a small shadow. Consequently, it really does have to make a bull's eye with the Sun. Most of the time, its shadow misses the Earth, and even when the shadow does reach the Earth, it covers only a small area.) If the Moon blocks out the Sun completely, we call it a total solar eclipse. If it only blocks out a section of the Sun, then it's a partial solar eclipse. Finally, because the Moon's orbit around the Earth is not perfectly circular, sometimes it will be perfectly aligned with the Sun, but still the solar disk will poke out around the edges. Then we have an annular solar eclipse. Because the Sun is so bright, unless it is totally eclipsed, it will be too bright to see with your eye. In fact, in most cases, you'll barely notice anything happening at all! Total eclipses are very rare, totally spectacular, and only last a couple of minutes. If you can, take a trip to see one. (But be prepared for crowds along the path of totality.)
About twice a year, the Moon will cross the ecliptic at a location exactly opposite that of the Sun. When this happens, the Moon will get in the Earth's shadow. This is a lunar eclipse. (The Earth is substantially bigger than the Moon, so it's shadow is bigger. Hence lunar eclipses aren't all that rare.) Although the Moon is being eclipsed, it does not disappear completely. Some sunlight (mostly red light) makes it through the Earth's atmosphere to the Moon. Consequently, when the Moon is eclipsed, we see it as a dull, red orb.