How big are red giants? How is their size determined?
The answer depends on what you mean by size
If you mean the mass well it can vary from 0.3-8 solar masses, 1 solar mass is about 2×10^30 kg.
How the mass is measured is all approximate numbers and it is not completely accurate because the stars are far away and cannot be accurately measures so they measure binary star systems stars based on their orbit of each other and orbital speed because measuring binary system stars are easy, so then they look at non-binary system stars of similarity and measure them off that which is approximate.
That is one way, but there are other ways they are measured such as the Hertzprung-Russel Diagram (search it up to see it if you need) using things such as age, luminosity, radius/diameter.
Radius/Diameter. That's the other thing your quest could mean by size the radius of a red giant can be anywhere between 100 million and 1 billion kilometres and continuosly growing.
Diameter is much hard to find because of diffraction making it much hard for methods such as using a telescope to measure than multiplying, or lunar occultations which are also not very common but these methods will give rough measurements.