The distance to the nearest star is about 4.2 light years. The standard baseline for parallax measurements is the radius of the Earth's orbit which is 8.5 light minutes. This means that the distance is about 267,000 times the Earth-Sun distance. We do not actually measure the distance to 1 part in 267,000 however. At the distance of Proxima Centauri, if we were to photograph its position 6 months apart, we would see the star shift position relative to the background stars by 2 x 1.3 arcseconds or 2.6 seconds of arc. This is because 4.2 light years equals 1.3 parsecs so that a shift of 1 Astronomical Unit ( the radius of the Earth's orbit) causes an angular shift of 1.3 arcseconds.
If you hold one finger at arms length in front of your face and look at it first with the left eye closed, and then with the right eye closed, its position will shift relative to things on the far wall. If your eyes were separated by the diameter of the Earth's orbit, as the photographic plates are, the shift will be 2.6 arcseconds of arc at a distance of 4.2 light years. For more distant stars, or for shorter time baselines, shifts of thousandths of an arcsecond are possible.
Recently, George Gatewood and Joost de Jonge at the Allegheny Observatory used a specially-designed instrument to determine the distances to Vega and Altair. The new results give a distance to Vega of 25.1 +/- 0.15 light year, and Altair of 16.62 +/- 0.065 light years. Typically, stellar distances are only known to about 10 percent accuracy, that is, 1 part in 10! These new measurements correspond to 1 part in 250 or so. The Hipparchos Satellite has completed astrometry of some 100,000 stars accurate to 0.002 arcseconds. This means that thousands of stellar distances will now be determined to 1 part in 100 or better for stars closer than 16 light years, or 1 part in 10 out to 160 light years.