For both position and flash period measurement, you need the following equipment:
A portable battery powered tape recorder with fresh batteries is most useful for recording observer commentary and for later flash period reduction. For positional measurements, you also need a short wave radio tuned to a time signal station. For faint objects and very accurate positional measurements an 11x80 binocular can be desirable.
Prediction software is widely available in the amateur community. Orbital elements of satellites are needed to calculate predictions. USSPACECOM regularly publishes orbital elements of almost all satellites. These elements are available in electronic form - follow these pointers to prediction software and information on obtaining orbital elements.
The orbital elements are fed into a computer program, yielding predictions. All satellites visible from the observing place and in the chosen observing interval are listed. Usually Right Ascension, Declination and/or elevation and azimuth of the satellite are given at several times during the pass.
If the satellite is not very bright it is difficult to use only azimuth and elevation as coordinates. In most cases it is more practical to use the Right Ascension and Declination to draw the track of the satellite in a star atlas. Choose an easy reference point along the orbit, such as a bright star, between two stars, etc.
The predicted track can deviate from the true one, as the orbital elements are not always very recent and can change considerably due to the influence of the Earth's atmosphere (in turn dependent upon the varying solar activity). Orbital corrections of active satellites can also spoil the picture.
Fortunately, for most satellites this is only a matter of at most one minute in time and one degree in position. However, for satellites in an orbit lower than 300 km or for manoeuvrable satellites this can get up to half an hour in time and several degrees in position. Most rocket stages can be predicted fairly accurately for longer than a month. For the Internation Space Station and the Space Shuttle on the other hand, predictions lose accuracy very rapidly.
A few minutes before the passage of the satellite, you start to watch the selected area of the star atlas. To anticipate deviations from the predicted track, you should "sweep" or "scan" with your binoculars in a direction which is perpendicular to the predicted track.
Around the calculated time, the satellite (hopefully) appears in your field of view. You can then proceed to make either rotational or positional measurements.