To measure precisely the frequencies of the oscillations is a quite complicated affair. Sound does not carry through the vacuum between the Sun and the earth. We have to `listen' to the oscillations by looking at the motions of material on the surface of the Sun. Observations can be done using various techniques : one can measure the oscillations in the light intensity over the solar disc, but most often the observations are done by measuring velocities using the Doppler effect, which makes it possible to take Doppler images of the solar surface.
A more recent development is to use a network of smaller, identical telescopes placed around the globe. Two of such networks are the Global Oscillation Network Group (GONG) and the Birmingham Solar Oscillations Network (BiSON). In such an international network there are always one or more telescopes, for which the Sun is above the horizon, so that the network of telescopes can observe the Sun 24 hours per day. An alternative is to have a satellite looking permanently at the Sun, which has the advantage that the earth's atmosphere (clouds !) doesn't interfere with the observations. The Solar and Heliospheric Observatory (SoHO) is such a satellite.
Different oscillation modes produce different patterns of vibration on the image of the Sun. Each mode of vibration has a characteristic pattern of node lines over the disc where the amplitude is always zero. We actually use that to identify the modes, but because there are very many vibration modes on top of each other at the same time, these patterns get jumbled together so we have to disentangle that to find out what pattern belongs to what frequency.
The result of this analysis can be shown as a colour-coded diagram which shows the strength of the oscillations as a function of degree l of the pattern and of the frequency.