We've talked about the optics that go into telescopes. However, it's clear that these optics need to be supported in some structure and kept in alignment with each other. The support structures needed are really an engineering issue (and a challenging one for large telescopes), and we won't disucss it here. In addition to supporting the optics, the structure also needs to be capable of tracking astronomical objects as they move across the sky because of the rotation of the earth.
There are two main different sorts of telescope mounts found in observatories: the equatorial mount and the altitude-azimuth (alt-az) mount. The equatorial mount is by far the most common for older telescopes, but the alt-az design is being used more frequently for newer, especially larger, telescopes. In the equatorial design, the telescope move along axes which are parallel and perpendicular to the polar axis, which is the direction parallel to the earth's rotation axis. In such a mount, tracking the earth's rotation only requires motion along one axis, the one perpendicular to the polar axis, and the tracking motion is at a uniform rate. In the alt-az mount, the telescope moves along axes which are perpendicular and parallel to the local vertical axis. With this mount, however, tracking of celestial objects requires motions of variable speed along both axes. An additional complication of an alt-az mount is the fact that, for a detector which is fixed to the back of the telescope, the image field rotates as the telescope tracks an object. Note, however, that the telescope pupil does not rotate with the object.
An equatorial mount is much easier to control for pointing and tracking. However, from an engineering point of view, it is much more demanding to construct, especially for large telescopes which have significant weight. The engineering complications generally result in a significantly larger cost than for an alt-az design. An alt-az telescope, however, has a significantly more complex control system, and must have an image rotator for the instruments.
Regardless of mount type, the mount is never built absolutely perfectly, i.e. with axes exactly perpendicular, exactly aligned as they should be, totally round surfaces, optics aligned with mechanics, etc. As a result, a telescope does not generally point perfectly. However, many effects of an imperfect telescope are quite repeatable, so they can be corrected for. This corrrection is done by something called a pointing model, which records the difference in true position from prediction position over the sky, and, once derived, the pointing model can be implemented to significantly improve pointing. A good telescope points to within a few arcseconds after implementation of a good pointing model.
Related to pointing is tracking performance. The issue here is how long the telescope can stay pointed at a given target. You can consider this question as how well the telescope can point over the area of the sky through which your object will drift. Since your required pointing stability should be significantly less than one arcsec, so that tracking does not degrade the image quality significantly, almost no telescopes have sufficiently good pointing to track to within an arcsecond for an arbitrarily long time. Most telescopes can track sucessfully for several minutes, but will give significant image degradation for exposures longer than this. Consequently, most telescopes/instruments are equipped with guide cameras, which are used to continually correct the pointing by observing an object somewhere in the field of view of the telescope (possibly the object you are interested in, but usually not, since that's where your detector is looking). These days, most guiders are autoguiders, meaning that they automatically find the position of the guide object, compute the pointing offsets needed to keep this object in one position, and send these offsets as commands to the telescope. The observer generally just has to choose a guide object for the autoguider to use, though they also may have to adjust the guide camera sensitivity or gain to insure that the guide star has a strong signal. These days, many autoguiders can automatically find guide stars from some on-line catalog (e.g., the HST Guide Star Catalog, which catalogs stars down to V 14). However, if one is taking long exposures and knows that they'll need to use guide stars, make sure to find out whether such a facility is available ; if not, it may still be possible to find guide stars in advance of your observing run, e.g., from the sky survey. If so, you should seriously consider doing so, as it can take a frustratingly long amount of time to search for a guide star at the telescope in real time. Since telescope time is heavily oversubscribed at most facilities, you really want to maximize your efficiency, and doing so is a large part of what will make you a ``expert'' observer.