There are several ways in which astronomers study the sun. Of course, the sun is too bright to study by looking at it directly. Therefore, examining the sun involves the use of specialized telescopes, satellites, and other measurement equipment. The sun puts out a lot of radiation. Specially modified radar systems are used to study this. Research satellites can take a lot of close-up measurements. This includes close looks at the sun's corona and taking detailed gravitational observations.
When using telescopes, astronomers use specialized filters that block out harmful light. This allows astronomers to make close up observations of the surface of the sun. With these telescopes, they can see things like solar flares and observe color changes on the sun's surface.
Things get more complicated when trying to understand the interior of the sun. The sun is too dense to be viewed visually. Therefore, astronomers employ a method called helioseismology to get an understanding of the sun's interior. This involves studying the sound waves that the sun creates. Waves of sound bounce around inside the sun, and observing their effects gives scientists an understanding of the overall composition of the sun. As sound waves bounce around the interior of the sun, its outer surface vibrates. Studying these vibrations allows astronomers to discern the sun's interior density and composition.
Another method of studying the sun involves measuring the electromagnetic spectrum of the light the sun puts out. Different atoms fuse at different temperatures. Studying the wavelengths of the sun's light gives information as to its composition and temperature. The sun even puts out radio waves and neutrinos which give insight into its nuclear process.
Solar flares are best studied using satellites. The YOHKOH satellite, in particular, has several instruments that take close measurements of solar flares. This includes highly detailed images that are sent back to Earth for further examination.