Telescope alignment methods

Every telescope needs to be aligned before the first use or if the position of a telescope has changed. For accurate tracking of celestial objects and astrophotography, alignment of the telescope must be done correctly. Some computerized telescope mounts have no memory of the previous settings. These mounts need alignment every time the power is shut down.
The alignment methods differ depending on the type of mount.

Alignment method

The movement of an Altazimuth mount and an Equatorial mount (Source: http://math_research.uct.ac.za)

There are two basic types of mounts, and both have different alignment procedures.

Altazimuth mount alignment

Altazimuth mount uses vertical (altitude) and horizontal (azimuth) axis to locate the object in space. Manual altazimuth mounts don’t require any alignment, while computerized mounts do. 

Several different alignment methods can be used:

Equatorial mount alignment

An equatorial mount moves the telescope in two axes. One axis moves in the direction of east-west and the other in the course of north-south. So far, this movement is the same as that of an altazimuth mount. The difference is in compensating for Earth rotation – one rotational axis must be parallel to the north/south celestial pole.
For simple observation, a basic alignment is required. 

For someone interested in astrophotography and deep-sky objects, a more precise alignment is required.