When estimating the distance to a very distant object, our “baseline" between the two points of observation better be large, too. The most distant objects our eyes can see are the stars, and they are very far indeed: light which moves at 300,000 kilometers (186,000 miles) per second, would take years, often many years, to reach them. The Sun's light needs 500 seconds to reach Earth, a bit over 8 minutes, and about 4.1 hours to reach the average distance of Neptune, the most distant planet. A “light year" is about 1600 times further, an enormous distance.
The biggest baseline available for measuring such distances is the diameter of the Earth's orbit, 300,000,000 kilometers. The Earth's motion around the Sun makes it move back and forth in space, so that on dates separated by half a year, its positions are 300,000,000 kilometers apart. In addition, the entire solar system also moves through space, but that motion is not periodic and therefore its effects can be separated.
And how much do the stars shift when viewed from two points 300,000,000 km apart? Actually, very, very little. For many years astronomers struggled in vain to observe the difference. Only in 1838 were definite parallaxes measured for some of the nearest stars --- for Alpha Centauri by Henderson from South Africa, for Vega by Friedrich von Struve and for 61 Cygni by Friedrich Bessel.
Such observations demand enormous precision. Where a circle is divided into 360 degrees (360∘), each degree is divided into 60 minutes (60')--also called “minutes of arc" to distinguish them from minutes of time--and each minute contains 60 seconds of arc (60"). All observed parallaxes are less than 1", at the limit of the resolving power of even large ground-based telescopes.
In measuring star distances, astronomers frequently use the parsec, the distance to a star whose yearly parallax is 1" --- one second of arc. One parsec equals 3.26 light years, but as already noted, no star is that close to us. Alpha Centauri, the sun-like star nearest to our solar system, has a distance of 4.3 years and a parallax of 0.75".
Alpha Centauri is not a name, but a designation. Astronomers designate stars in each constellation by letters of the Greek alphabet --- alpha, beta, gamma, delta and so forth, and “Alpha Centauri" means the brightest star in the constellation of Centaurus, located high in the southern skies. You need to be south of the equator to see it well.