Reddit mentions of Parallax: The Race to Measure the Cosmos (Dover Books on Astronomy)

First came the size of the Earth. That was done around 240 BC by Eratosthenes.

Then a whole lotta nothing happened till Kepler who figured out some rough orbits for planets that was proportional, but didn't have exact figures. But he did have the P^2 = a^3 thing going which was cool since it meant if we could get the orbital distance from the Sun for one planet, we could standardize the formula and make it work for all planets.

Then Newton came along and tweaked Kelper's 3rd law by noting it wasn't quite that simple because masses of the objects mattered. But barely since the Sun is so much more massive.

Then in the late 1700's, Venus was set to transit the Sun a few times. By observing the transit from different points on Earth, astronomers were able to use parallax to determine the exact distance to Venus and the Sun. By 1771, French astronomer Jérôme Lalande had come up with the distance to the Sun being off by only 2%. (Good book on the topic)

Once we knew the Earth-Sun distance, we could again use parallax to get distances to nearby stars by observing them when Earth was in different parts of its orbit for a long baseline. The hardest part was knowing which stars to choose as a target since many stars don't show much as they're far away. At the time, many astronomers thought all stars were the same intrinsic brightness and therefore, brighter ones must be closer. Turns out not so much. Ultimately, the first successful attempt was in 1838 for 61 Cygni. Several others followed soon afterwards. (Another book on that topic)