My Meade telescope needs to be calibrated each time it is powered up. The red dot finder blinks and the hand keypad tells which star should be aligned. Then you go to a second star. After this is complete, the telescope is calibrated and you then say "Go to Jupiter" or "Go to the Andromeda Galaxy" and so on.
The settlers from Ark I landed on a habitable world in the Alpha Centauri system. They called their world New Earth although later the Vuduri renamed it to Helome. Silas Hiram was a farmer who brought a telescope with him. The makers of the telescope were kind enough to modify the internal database so that he could use the red dot finder from Alpha Centauri.
Since Alpha Centauri is so close to Earth, cosmically speaking, relatively few adjustments needed to be made and most of the constellations appeared more or less the same as seen from Earth. The one major difference is that the Centaur was missing one star in his foot. That star was Alpha Centauri.
Sol and Earth would appear as an extra star between the constellations Perseus and Cassiopeia. Nothing remarkable other than the fact that it was Earth.
The constellation of Orion appeared more or less identical with the except that from the perspective of Alpha Centauri, the star Sirius would appear to be part of that constellation. Sirius was the second star that Silas had to use to align his telescope. It forced him to look for Orion and that was when he noticed that Alnilam was gone. This singular act caused a cascade of actions spanning 14 centuries, culiminating with the "defeat" of the Stareaters on Tabit and the peace treaty of Earth.