The two main methods to detect the solar p-mode oscillations, which have a period of about 5 minutes (so frequency of ~3 milliHertz) are line of sight Doppler shift and change in irradiance.
The Doppler method works by measuring the intensity of light in (normally) two narrow regions either side of a prominent spectral line in the Solar spectrum and using this change to measure the velocity shift caused by the oscillations (once the solar rotation is removed). The ground-based GONG instrument uses the Ni I at 676.8nm, BiSON network and the GOLF instrument on the SOHO spacecraft both use the sodium D lines. After isolating the light around a suitable spectral feature, then you can either use a Michelson interferometer to get a velocity image of the shifts across the surface (GONG and MDI on SOHO) or a disk-averaged velocity, treating the Sun as a star (BiSON and GOLF on SOHO). The difficulties are in keeping everything stable so that the measured shifts only come from the Sun and not the instrument. For example GONG note that their optical elements are stabilized in an oven to the order of 0.00001 K.
The irradiance method simply involves measuring the disk-integrated intensity of the Sun and watching for changes caused by the oscillations. However fluctuations in the Earth's atmosphere make this very difficult to do from the ground and the most successful has been the VIRGO instrument on the SOHO spacecraft.
The imaging instruments have a resolution of about 2" (MDI) to 5" (GONG) so return velocity data at approx. 800,000 to 100,000 locations across the Sun. This allow the study of oscillations with very high degree (up to 1000) which have very small scale on the surface. The disk-integrated "Sun-as-a-star" instruments by comparison are sensitive to the low order oscillations.