Due to the rotation of the axis of the Earth, coordinates change with time. The reference point therefore slides around on the equator making one round in 25,770 years. The corresponding change of coordinates is given by the equations presented here. The change with time makes it necessary to give coordinates at a given epoch. Presently, the most common reference data is the year 2000, and the epoch is denoted J2000 (year 2000 in the Julian calendar).
Other changes of coordinates is given by the aberration, the yearly parallax and the proper motions. The aberration is common for all stars in a field, but it does have an effect, when the telescope has to pointed at a given target as offsets up to 20" can occur. Proper motions are small: of the order 1" per century except for a few fast moving objects. The parallax is of no significance for pointing to a star, but it does matter if very precise positions are needed, and the parallax is an important quantity, when it comes to the measurement of distances to stars.
Earlier when trying to locate a given object in the sky, one would use a sky atlas or a collection of photographic plates to make a finding chart to bring to the telescope. Comparing the piece of sky seen in the eye piece or on the CCD image with the finding chart, an identification of the object could be made, so that the right observations were made.
Now, things has become a lot easier. There are digital maps that can be consulted using internet web programs to display or print small sections of the sky centered on a given target.
One such service is provided by ESO as the Digitized Sky Survey.
An image might look like this 7' by 7' piece of the sky.
Large databases of objects are kept at various institutions. One of the largest collection of data is stored in Strasbourg by the CDS (Centre de Donnees astronomiques de Strasbourg).
One of the very useful tools is a database of information about individual stars under the name SIMBAD. Here one can type in the name of a star and get it's position and other parameters for the star. The information also includes a complete? list of references. In addition one can search for stars fulfilling search criteria, such as being brighter than magnitude 2.0.
ESO and NASA also store all data in large archives, which one can consult. ESO has even created a concept call the Virtual Observatory, which rely only on existing data in the ESO (and other?) archives. The Hubble Telescope data are stored likewise.
Stars are denominated in many different ways. SIMBAD will give you a long list of identifications for any single star. Here are some examples:
Other objects have different names
The time used in astronomy is the Universal Time UT (or UTC), which is now based on atomic clocks and accessible by various internet or radio connections (also via the GPS system). Earlier the time was based on the rotation of the Earth, which is not a very good definition as the rotation slows down. Later time was attached to the movements of the planets, as the planetary system was considered to be an inertial system. The was called the Ephermeris time.
Nature does supply some natural clocks, which might surpass even atomic clocks in terms of precision. Some millisecond pulsars emit pulses so regularly, that they might be the best clocks available.
Sidereal time (ST) is defined as the time angle of the point of Aries (Vernal equinox), which means that the ST tells which Right Ascension you have in the south at a given time. When you are picking stars to observe during the night, you try to select stars with positions matching the ST.
Remember that the Sun has Right Ascension 0h at vernal equinox. Thus you should observe targets with Right Ascension around 12h around that time. Also, remember that Right Ascension of stars to be observed increases during the night as ST increases.
Due to the movement of the Earth around the Sun and due to the rotation measurements of events in the sky will vary in time as the distance to the target changes. Therefore one should correct the time to what would be measured at the center of gravity of the solar system og at least the center of the Sun. These times are called Barycentric time and Heliocentric time.
It is unpractical to measure time by giving a date and a time of day. Instead one uses the Julian time. The time starts at noon on Jan 1, 4713 BC. The Julian Day beginning on Jan. 1, 2000 is JD 2 451 545. If you have your time in UT, you can often find routines to calculate the JD. If you then want to get the barycentric time you get the HJD. Finally there is another definition modified Julian Date MJD = JD - 2 400 000.5, which is more convenient as it has less digits. It also changes at midnight.