The birth of a star is located in Large nebulae and during most of its lifetime, it emits radiation due to the nuclear fusion occurring at its core. Considering the stars are so far away, their motions cannot be observed unless they are close enough to detect a shift in their positions through Stellar Parallax. Due to the lack of relative motion observed from earth, even after hundreds of years, star maps can be drawn to show their approximate position in the skies. However, as the earth rotates around its axes, the star's positions change during the night. And also, since Earth also orbits around the sun, patterns we see shift every night. During the day, if necessary, the stars can be detected using a radio telescope.
Distance to stars that are relatively close to the Earth can be measured trigonometry in the stellar parallax method. Parallax is the displacement in the position of an object compared to its background once viewed from different positions 6 months apart. Parallax angles are fractions of arcseconds which are 2600 arcseconds at an angle of one degree. However, for stars further away from 100 parsecs, the uncertainty is too high (parallax angle is too small, less than 0.01 arcseconds) to use the stellar parallax method thus other methods must be used.
Otherwise, one can identify a star with a known power and relate it to the intensity of radiation received on Earth. Red-shift measurements can also be used to measure farther distances such as to galaxies. Considering meters and kilometers are too small of measurements, another series of distance units are used for astronomy.
Definitions relating stars
A group of visible stars within a particular region is called a "Constellation". An example is Orion. Stellar clusters, however, are mobile and due to the gravitational forces between them, they move as a group. There are two types of clusters; Globular ones contain a large number of stars and thus the higher gravitational force between them forms a combined spherical shape. Open ones have fewer stars and thus do not have a specific shape due to the lower gravitational force.
The dominant nuclear fusion in stars is the fusion of hydrogen into helium as seen in the equation. Following the equation, 4 hydrogen nuclei lead to a decrease in mass and a release od energy of about 27 MeV. As stars age, heavier elements are incorporated. Stars in a Stellar hydrostatic equilibrium are said to be on the "Main sequence", meaning equal radiation pressure out as a gravitational force in. Considering the rate of energy radiated is equal to the rate of nuclear fusion, there will be an end once fusion supplies run out and the equilibrium is disturbed.
Binary stars are pairs of stars close to one another but too far away from Earth to be detected as two separate stars. Thus they have observed in detail to find out. If they are binary, the intensity will change periodically as one star eclipses the other and the radiation with have opposite Doppler shift in they are moving in opposite directions.
Galaxies have many more stars than stellar clusters and rotate about its own center of mass. They are classified as either, principally, elliptical, spiral, or irregular. All the stars we seem from Earth are located within our own galaxy known as the Milky Way. Even galaxies are usually in clusters and again due to the high gravitational force, they have a spherical shape. Our Milky Way is in a cluster of about 50 galaxies called the Local Group. But, that number can reach hundreds and even thousands, and those are then called Superclusters.
Planets are also mobile, orbiting elliptically in a path around a distant sun. The period of the orbits varies depending on the mass and distance from the planet to the sun. Natural satellites orbit around planets and are called "Moons". Other smaller objects also orbit the sun, mostly located between Mars and Jupiter and they are called Asteroids. Comets are made out of ice and dust with longer periods and elliptical paths. The tail that is formed once the comet passes the sun is due to the solar radiation heating up the comet.
Luminosity & apparent brightness
If the side and the surface temperature of a star are known, its luminosity (power) can be determined from Stefan-Boltzmann law P=eσAT^4. The equation can be rewritten to L=σAT^4 (unit: W) assuming the star behaves as a perfect black body with an emissivity of 1.
The intensity of radiation received before Earth's atmosphere affects it is called apparent brightness. Assuming radiation spreads equally in all directions and no energy is absorbed in interstellar space, the equation is Apparent brightness can be calculated from b= L/4πd^2 (unit: Wm^-1). For more distant stars, uncertainty becomes significant.
Images from: Physics book - John Allum and Christopher Talbot - Second Edition - Hodder 2017