Astronomy is the oldest science, and the oldest use of astronomy is very likely navigating by the stars. This craft dates back to prehistoric times among humans, and some amazing feats of path finding have been achieved by primitive tribes such as the Maori, using only the sky as a guide.
Even in today's modern world, celestial navigation is still relevant not only for astronomers but also as an important part of a navigator's formal training for both sailors and pilots.
The Equatorial Coordinate System is generally the preferred way astronomers use to keep track of the positions of objects in the sky. Astronomers imagine that the Earth is surrounded by a large sphere called the celestial sphere. The Earth's equator and the plane of the Earth's orbit are projected onto this sphere.
The plane of the Earth's orbit is called the ecliptic when it is projected onto the imaginary celestial sphere. The Earth's axis of rotation is at an angle of 23.5° to the plane of the Earth's orbit, so the celestial equator and the ecliptic are also at a 23.5° angle to each other.
The plane of the ecliptic and the plane of the celestial equator intersect twice a year, around March 21st and September 22nd. The points on the celestial sphere where this occurs are called the vernal equinox (in March) and the autumnal equinox (in September).
The following videos demonstrates the concept of the ecliptic:
The Equatorial Coordinate System uses two measurements, right ascension and declination. Right ascension (abbreviated RA) is similar to longitude and is measured in hours, minutes and seconds eastward along the celestial equator. The distance around the celestial equator is equal to 24 hours.
Declination is similar to latitude and is measured in degrees, arcminutes and arcseconds, north or south of the celestial equator. Positive values for declination correspond to positions north of the equator, while negative values refer to positions south of the equator. The declination of the north celestial pole is 90° 0' 0" and the south celestial pole's declination is -90° 0' 0". The equator is 0° 0' 0".
The position of an object is stated with the right ascension first, then the declination. For example, the bright star Sirius' position is RA: 6h45m8.9s Dec: -16°42'52.1".
The advantage of the equatorial coordinate system is that it expresses the position of a star or galaxy in a way that is independent of the observer's position on Earth. However, the right ascension and declination of a given object change slowly over time, mainly due to a phenomenon called precession.
Precession happens because both the ecliptic and the equator are slowly moving, as a result of tidal forces from the Sun, Moon and planets. The main effect is from the Moon, which makes the celestial pole orbit around the ecliptic pole once every 26,000 years. So along with the RA and Dec of an object, you will usually see the date, expressed in years, when those coordinates were approximately valid. This date, or "epoch", defines the precessing equator and equinox used to construct the star catalog. Common examples are B1950.0 and J2000.0, where the B and J stand for slightly different sorts of year.
The changes to the coordinates happen slowly enough that successive generations of star catalog are 50 years apart. However, the most recent star catalogs, which are equinox J2000.0, will probably be the last in the sequence: there are unlikely ever to be equinox J2050.0 catalogs, because of the adoption of the International Celestial Reference System (ICRS).
The ICRS broke the connection between catalog positions and the Earth's motion, and is defined instead by a set of quasars. For continuity, the ICRS was set up to be a good approximation to the equinox J2000.0 system, so in effect the catalog RA,Dec system has been frozen at J2000.0.
Stellarium and Google Sky both tell you the coordinates of celestial objects. For practice you can try using one of the programs to find the following: