CTIO at sunset (NOAO/AURA/NSF)

HOW DO WE STUDY STARS?

Electromagnetic Radiation (X-ray, UV, Optical, IR, Microwave, Radio)
Particle Emission (Neutrinos, Stellar Winds, Cosmic Rays, ...)
Gravitational Wave Radiation
...

ASTROPHYSICS IS A DIFFICULT EXPERIMENTAL SCIENCE, WHY?

Stars are distant which makes ordinary experiments impossible. The nearest star is Proxima Centauri at a distance of 4.3 light years ~ 40 trillion kilometers. (One light year is the distance a beam of light travels in 1 year ~ 9.3 trillion kilometers.) Traveling at the speed of the typical interplanetary probe, ~ 20 kilometers per second, it would take 70,000 years to reach Proxima Centauri!

We cannot control stars, in particular, we cannot design the types of experiments we would like to perform on stars; We must take what nature gives to us, that is, for the most part we passively observe the sky.

HOW DO WE OBERVE STARS?

Electromagnetic Radiation
Most observations of Celestial Objects are made using Optical Telescopes located at ground-based (e.g., Kitt Peak National Observatory , Cerro Tololo Inter-American Observatory , National Solar Observatory, ...) and space-based orbiting observatories (Webb Space Telescope). Optical light will be defined in a second. For now, take it to mean the type of light to which our eyes are sensitive.
A ton of information about the Universe has been gleaned from optical observations, however, much more can be learned if we consider more than just optical light [objects in the Universe produce many other forms of radiation. Collectively, the overall radiation phenomenon is referred to as Electromagnetic radiation (EM radiation). Until recently the complete EM spectrum was not utilized because

Most types of EM radiation cannot penetrate the Earth's atmosphere and so do not reach the surface of the Earth. The major windows fall in the optical (visual portion) of the spectrum and in the microwave and radio portion of the spectrum. There are also windows in the IR. Fortunately for us, the gamma-ray, x-ray, and most of the UV is blocked by the atmosphere of the Earth shielding from these forms of high-energy electromagnetic radiation.

Today, because we can place telescopes into orbit about the Earth, we are able to study stars across many portions of the EM spectrum and to get above the blurring effects of the atmosphere (the effects of seeing). The most spectacular of these missions is the Webb Space Telescope.

Webb Space Telescope (WST)
The WST is a large segmented (18 pieces) space telescpe, total diameter 6.5 meters. The Hubble Space Telescope was only 2.4 meters in diameter. The largest Terrestrial telescopes are 8 to 10 meters in diameter. The WST is valuable because:

It is above the atmosphere and can observe from the visible light to the mid-infrared, wavelengths ranging from 0.6 microns to 28.5 microns.
It is above the blurring effects of the atmosphere (seeing) and can form very precise images. Why is this important? There is a low-level background in the Universe caused by distant galaxies, stars, and gas and dust, which we always pick-up in addition to our targets. If an image is small, we can stop down the opening on our detector and only allow in a small part of the background. If the image is large (because of seeing), we must open up the diaphragm on our detector which allows in more of the background. This makes our detectors much less sensitive for the detection of faint objects. See Section 5.4 for ground-based telecopes which are starting to approach the image quality given by the WST.

Material (Particles) From Stars
We also study stars using the matter (particles) they produce, e.g., the Solar Neutrino Experiments studies the particle emission from the Sun (see Topic 1).

Gravitational Radiation
There are also experiments designed to detect the gravitational radiation from compact stars and other Celestial Objects.
The opening up of the EM spectrum and the study of other forms of Celestial emissions have substantially enhanced our understanding of Celestial objects of all kinds.