The above diagram indicates the general layout of the mechanics of the night sky. If you projected a line through the Earth from the south pole to the north pole, and on into space, that line would appear to point directly at Polaris, or as we commonly call it, the north star.
All of the stars in the northern hemisphere rotate around Polaris during the course of the evening due to the Earth's rotation. To counteract this, one needs only line the Right Ascension axis of the equatorial mount at this magical center point, and all movements can be counteracted by turning the telescope on one axis. The Right Ascension axis is the one that is connected to the tripod. The one that is connected to the telescope and the counterweight shaft is the Declination axis. Every object in the sky has a co-ordinate given in hours, minutes and seconds of Right Ascension, and degrees, minutes, and seconds of Declination. Objects above the celestial equator have positive degrees of Declination and objects below have minus degrees of Declination. You go from 0 to 90, and 0 to -90 degrees going north of the celestial equator and then south of the celestial equator respectively. There are 24 hours of Right Ascension in a full circle.
You can do a simple alignment of your astronomical telescope's mount by placing the mount with the counterweight down, tube up. Now rotate the telescope until the tube is exactly in line with the Right Ascension, or polar, shaft of the mount. You can turn the base of the telescope in azimuth until it is in line with Polaris, and then finally, adjust the latitude setting on the equatorial head until the telescope is directly aimed at Polaris. This is the most simple method of polar aligning a telescope, and is sometimes called the home position on GoTo equatorial mounts.
Once you have roughly aligned the scope, you can use the hand controller to pick two stars, center them in the field of view, and hit enter to tell the electronics that you are pointed at them. Aligning a GoTo mount is really this easy, and once you've done it once, you can remember how to do it time and time over.
Another far more precise method uses the declination drift method, where you choose stars near the celestial equator both at the meridian, and at the eastern horizon. I first discovered this method in a 1977 Sky and Telescope article by Robert Provin on doing precision astrophotography. It has never let me down. You need a reticle eyepiece to do this, and you only move the telescope in Right Ascension to do this. The longer you can keep the star from drifting, the more precisely aligned your telescope will be. This method works great in an observatory, even when you can't see Polaris.
First, choose your star near where the celestial equator (i.e. at or about 0ยบ in declination) and the meridian meet. The star should be approximately 1/2 hour of right ascension from the meridian and within about five degrees in declination of the celestial equator. Center the star in the field of your telescope and monitor the drift in declination.
•If the star drifts south, the polar axis is too far east.
•If the star drifts north, the polar axis is too far west.
Using the telescope's azimuth adjustment knobs, make the appropriate adjustments to the polar axis to eliminate any drift. Once you have eliminated all the drift, move to the star near the eastern horizon. The star should be 15 to 20 degrees above the horizon and within five degrees of the celestial equator.
•If the star drifts south, the polar axis is too low.
•If the star drifts north, the polar axis is too high.
The closer those stars are to the celestial equator, the more accurately your mount can be aligned. For long term use in an observatory, I will let it drift for 90 minutes, but you can speed this process up a lot by using a barlow lens because it really amplifies the drift. Remember to only make corrections in Right Ascension while doing this.
Some people like Dobsonian mounts. I have only ever used equatorial mounts, first without tracking, then with tracking, and finally with GoTo, which I absolutely love. Doing this simple procedure can let you see thousands of objects without frustration, and let you focus on enjoying your scope, rather than tracking it around the sky. I don't find an equatorial mount confusing in the least, either to operate or find objects with. Merely using one can teach you how objects appear to move in the night sky, much like the drawing above depicts. So before you go out and buy that big yard cannon that everyone recommends to newcomers, you might consider the convenience of having and using an equatorial mount. If you are going to do any kind of astrophotography, it is the only way to go. My blog's record is proof of that. If an 8 year old can use one without tracking, you can learn too. It really can deliver you a lifetime of amateur astronomy.