Great questions! We can find the distance of stars by using simple trigonometry! Astronomers observe distant stars at one point in the year, and again six months later when the earth is halfway around the Sun. By that time, the star of interest will have appeared to shift slightly when compared to even more distant stars. From this perspective, scientists can determine the (very small) angle between the Earth, the star, and the Sun. Then using simple trigonometry, they can determine the distance to this star. This technique is used in part to map out the shape of our Milky Way galaxy. A link is provided at the end of this answer.

To find the temperature of stars too far away to measure directly, we need to understand the relationship between heat and color. You may notice that, for example, a cool flame burns faint red or orange, but a hot flame burns bright blue. Analogously, scientists often use the color of a star to determine its temperature. They can classify the type of star by its color (and temperature). A red star, for instance, is about 3,500 – 6,000 F (2,000 – 3,500 C) whereas a blue star is about 20,000 – 50,000 F (11,000 – 28,000 C)! In fact, blue stars are classified as some of the hottest (and usually largest) objects in space. From looking at the composition of our Sun along with various other techniques, scientists make guesses as to the composition of other stars in our universe and conclude that, based on these high temperatures, the phase of the materials must be plasma.