I was reading all the characteristics of some random comet and I was wondering, how do we figure out the exact size, circumference, weight, etc. etc. of something so far away? Or how do we figure out how far away it is? Or what its surface is like? Among other things?
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Let’s start with how far away. Hold a candle close to you, and it will look bright. Put it very far away, and it will look dim. If astronomers look at the intensity of light coming from stars, then the distance can be estimated from that. But how do they know the distant stars can be considered similar light sources? After all, in the other example, a candle would appear different from a campfire. It turns out the properties of stars and their composition determine their emission spectra, and measuring how much light is around certain frequencies will give a picture of that. (Incidentally, this also gives information about relative speeds because of Doppler shifting.)
Once we know how far away it is, it’s a simple trigonometry problem to tell how big it is, as when it’s observed on a telescope, it spans an angle.
Its mass can be calculated if something is observed orbiting it – usually a large planet orbiting the star. The orbiting object is observed over a long enough time span, from which its orbital period and orbital radius can be calculated – the former by how long it takes to return to an initial position, the latter by the biggest sway in distance on each side of the star (again using trigonometry). Orbits follow very predictable patterns from Newtonian gravitation, from which the mass of the star can be determined. If the star’s wobble is detected, then using center of mass properties will tell how massive the orbiting object is; for example, if the star is 1000 times heavier than the planet, then the planet should orbit 1000 times the distance from the center of mass as the star from the center of mass.
All this requires powerful telescopes and some precision measurements, to say the least.