The stars appear to be fixed to the Celestial Sphere and since we are interested only in relative motion, we can imagine that the Earth is stationary and that the Celestial sphere is turning. The resultant motions are then rather simple. Because the stars do not move on the Celestial Sphere, they maintain constant distances from the rotation axis and so simply trace circles on the sky centered on the projection of the axis of rotation of the Earth onto the Celestial Sphere (that is, the North or South Celestial Pole).
The daily motions of all celestial objects (the stars, the Sun, the Moon, and the planets) follow this pattern. Note that the objects move from east-to-west across the sky which means that the Earth spins from west-to-east. Or, as viewed from the NCP, the Earth rotates in the CCW-sense.
To answer this question, we first define the horizon. Because we cannot look through the Earth, we can only see that part of the sky which is above the ground.
North Pole (latitude=90 degrees):
whether a star is circumpolar is determined by how close it
is to the NCP or SCP. Stars closer than the latitude of the observer
to the pole are circumpolar.
Equator (latitude=0 degrees):
so that, at intermediate latitudes, the diurnal circles are tilted with respect to the horizon. Stars that are within the latitude of the observer from the NCP never set. In Eugene, stars within 45o of the NCP are circumpolar.
Polaris, the North Star, sits right near the NCP. Consequently, the latitude of an observer is given by the altitude of the North star above the North point on the horizon.
The sidereal day is 23 h 56 m 4.091 s. The sidereal day is defined as the time it takes a star to make a complete trip around the sky. The Solar day is defined as the time it takes the Sun to make two successive crossings of the meridian:
If the Earth were stationary, then the Solar Day and the Sidereal Day would be precisely the same. However, we know that the Earth also revolves about the Sun. How does this affect the Solar Day?
Because the Earth roughly moves at a rate of (360 degrees)/(365.25 days) ~ 1 degree per day, the Earth will have moved 1 degree after 1 day. This means that in order for Sun to return to the Celestial Meridian, the Earth must turn roughly 1 more degree. That is, the Earth must turn ~1/365-th of the way around again to have the Sun reappear on the Meridian. This means that the Solar Day will be roughly 1/365-th times longer than the Sidereal Day.
If the Earth's orbital motion were steady with respect to the Celestial Equator, then this would be the entire story. Unfortunately, the Earth's orbital speed is not constant; it varies throughtout the course of the year because of the elliptical shape of its orbit and the mis-alignment of the ecliptic and the Celestial Equator. Consequently, the length of the Solar Day also varies throughout the course of the year. From a timekeeping standpoint, this is not acceptable and so the Mean Solar Day was defined to be the basis for timekeeping. The Mean Solar Day is the average length of the true Solar Day. The Mean Solar Day defines the clock day.
This is why the Sun sometimes appears to be late and sometimes appears to be early with respect to clock time. By early and late, I mean that the Sun does not cross the Meridian at the same time every day! This information is carried in the analemma (see the sun dial constructed by Bob Zimmerman and John Nichols in the Memorial Quad, across the street from Lillis Hall).