Telescopes will generally come with a library of objects, which includes information on where they are located on the celestial sphere.
There are two important pieces of information needed for the telescope to be able to locate objects from your Earthly location - Your position so that it knows its orientation relative to the celestial sphere, and the time so it can predict how that orientation will change.
When you initially set up your telescope, it will likely ask you first for the time, and then you will locate some easy to find objects. By finding three objects, the telescope will generally be able to understand its orientation relative to the celestial sphere.
At this point, it becomes trivial to find any object in its library, because it knows where the object is located, it now knows where it is, and it knows the time to adjust to changing in the Earth's orientation.
Even if power down your telescope, it takes very relatively little energy to track time and saving your location information is quite cheap. If the telescope can assume you're viewing from a relatively similar location, and it has kept track of the time, it has all the information it will need to find objects as soon as it starts up. As Colin said, if you change locations, you would then need to recalibrate as one of the key pieces of information the telescope is using would have changed.