The basic method of observation is to use predictions so that you can be looking in the correct direction near to the right time. A stopwatch with an accuracy of at least 0.5 seconds is essential. Set the watch by radio time signals or by the telephone system's speaking clock. The latter is more satisfactory method, since the stopwatch can be set just before observation begins.
Gauge the positions of a satellite by imagining a line drawn between two fairly close stars between which the satellite passes, or by imagining a vertical line drawn down from a particular star. In either instance, it is the precise moment at which the satellite crosses this line that is important. The stars can be identified from a star atlas, and it is a good idea to drawn a sketch map of the star field chosen and to indicate the satellite's track on it.
Observers find that identification of the position is not difficult; the great problem is the accurate timing of the transit of the satellite. As in all practical astronomical work, this is an example of the need for practice and constant repetition in order to produce reliable results.
Artificial satellites vary in brightness, depending on the height at which they are orbiting and on their size. They can best be divided into three classes; bright satellites visible to the naked eye - usually brighter than magnitude 3; those that are dimmer, with magnitudes between 3 and 9; and extremely faint satellites. With the unaided eye it is possible to see down to magnitude 6, although dimmer than magnitude 3 or 4, you will need to know where to look. Satellites dimmer than magnitude 6 require binoculars or a telescope if they are to be seen and, in any event, it is important to know where and when the satellite is expected to appear from tables published in some journals and daily newspapers.
Note: See Satellite Tracking for software to track satellite.