We first measure the angular size of the Sun and then note that
radius of the Sun ~ D x angle
We infer that the radius of the Sun is 696,000 km.
Finding the radii of other stars is more difficult. We cannot directly measure the angular sizes of stars in the above manner except for the largest most nearby stars using new modern interferometric techniques, such as the Very Large Telescope in Chile (see Betelgeuse (from APOD), and other interferometric techniques known as speckle interferometry and Michelson interferometry. To date, the most useful way of finding the radii of distant stars is to use binary (eclipsing) star systems.