How can we focus radio telescopes on a star when the earth is spinning? Reading about the Star KIC 8462852, it has been said that the SETI project turned its radio telescopes towards the star to search for extra terrestrial radio signals as the star had strange fluctuations in light. How can we point from earth a radio telescope towards a star which is 1480 light years away whilst the earth is spinning at 1675 km/h and keep it focused or, in the case of a radio telescope, aligned in order to try and receive radio waves??
Part of the answer that I suspect the original questioner needs is that although the Earth is indeed spinning very fast, the amount the surface of the Earth moves relative to an astronomical object is tiny.

So you put motors in the base of the telescope so that it slowly turns to look at the same patch of sky.   You don't need to refocus because telescopes are looking at objects so far away that focus doesn't matter.  You don't need to do anything else because the Earth's movement is smooth and continuous, and it's not about how fast you're moving, it's about how quickly you're turning.  In our case, one complete circle every 24 hours which is pretty slow.

Focus at infinity just means that you set the focus of the telescope so that an object which is infinitely far away would be in perfect focus.  It depends on the quality of the telescope, but the practical difference between focus at infinity and focus at the actual distance disappears after a few miles or so.  At the distance of stars, there is essentially no difference at all.