There are two basic types of telescope mountings; these are the altazimuth and equatorial mountings. There are variations on quality and extras, but the telescope mountings are all based on these two standards.
The altazimuth is the simpler of the two mountings, and also the cheaper. It consists of a stand, which can move through two axis. This allows your telescope to move up and down (altitude), and from side to side (azimuth).
Although this may seem to be a perfectly acceptable amount of movement, you will soon find that when you are tracking a planet or star, the astronomical body moves at an angle to the horizon. To combat this angle, the equatorial mount not only moves through the two angles, but the telescope can be set at an angle to the horizon. This means that the telescope, when tracking an astronomical object, can arc in relation to the movement of the earth, and keep the object in view.
The German equatorial mounting is a variation on the equatorial mount, and has a counterbalance that allows the telescope to be moved to almost any angle. This givesthe telescope access to all parts of the sky. This varies from the fork equatorial mount in that although it does not require a counterbalance, it does have some restriction to viewing the sky due to the mounting itself getting in the way.
A refractor or a Newtonian reflector telescope is usually mounted on a German equatorial mount. These can be motor powered, which will let you get on with the job of studying the sky. Such a telescope mounting can even be computer driven, which does cost a lot more money, but is a lot of fun. A computer powered telescope mount can be programmed to locate and follow a specific object with great accuracy. As long as you set up your home position correctly.
The altazimuth mount is usually found supporting large Dobsonian telescopes. Because these mounts are so simple, they allow you to concentrate your cash on the larger telescope.
The choice of mount really depends on what you want to use your telescope to look at, and what telescope you want to buy. If you have a small budget, of, say three hundred pounds, you can buy a good quality 8-inch Dobsonian telescope with an altazimuth mount. The same amount of money may only buy you a 4 or 6-inch refractor with a manual German equatorial mount.
To find out what mount suits your star gazing style, you have to decide what telescope you want. If you own a large Dobsonian then don’t despair, there are plans available on the Internet that show how to mechanise the basic altazimuth mount.
A word of warning though, if you do decide to build or buy your own telescope mount, take into account the weight that the stand and mount has to have to counteract the weight of the telescope. To support a large 16-inch telescope on a German equatorial mount, you need a counterweight of over 22kilos. Not exactly a very portable telescope, but certainly a dream machine for the amateur astronomer.