Hi Matt.
There are no fundamental differences between the various types of telescope mounts at all - they all rotate the scope about two orthogonal axes. However, those axes can be aligned differently with respect to the earth.
With an alt/az (or Dobsonian) mount, you aim the scope like you would aim a cannon, by rotating it in both a horizontal plane and a vertical plane. When you track a star, you must move it in both axes, since the star appears to move in both elevation and azimuth as the earth rotates.
In an Equatorial alignment, the "horizontal" plane of the alt/az mount is tilted using a wedge of some sort so that the axis of rotation is made parallel to the rotation axis of the earth. Then, when you track a star you only need to move the the scope in that axis (called the right ascension axis) to compensate for the rotation of the earth - you do not need to use the other axis (called the declination axis) at all ..... provided the mount is properly aligned.
The Eq alignment also removes the field rotation problem of an alt/az mount, which causes objects to appear to slowly rotate in the eyepiece as you track them. This means that Equatorial mounts are best for astro-photography.
However, if you are using a telescope with a side mounted eyepiece (eg a Newtonian), an equatorial mount can place the eyepiece in almost any position as you slew around the sky - and not necessarily one where you can put your eye - so an alt/az mount will be a better choice for visual use with such a telescope - this is the Dobsonian arrangement.
buying a cheap eq mounted scope would be an excellent way to understand how they work - a bit of messing around will be much more informative than words. And maybe read this
http://members.optusnet.com.au/~beep...0Telescope.pdf
regards ray