How do I balance my telescope on an Equatorial mount?

Your equatorial mount must be balanced in both axes, if you want to be able to get the best performance out of the mount. To accomplish this, you must:

1. For the RA axis, lock the declination axis so that the tube is parallel to the polar axis.
2. Unlock the RA (polar) axis and rotate the scope until the counterweight shaft is horizontal. Slowly release the scope. If it swings either way, it needs to be rebalanced. Carefully move the counterweight(s) towards the mount if it is heavy on the weight end, or away from the scope if it is heavy on the tube end. Repeat the balance check and adjust again as necessary until there is no or minimal swing.
3. For the declination axis, place the scope so that the counterweight is low, tube is high and lock the RA axis.
4.  Push the tube so that it is parallel to the ground. If it swings either way, carefully loosen the tube clamps and push the tube in the rings away from the heavy end to re-balance. Repeat the balance check and adjust again as necessary until there is no or minimal swing.

NOTE: You want to make sure you are not perfectly balanced in Right Ascension, the reason is due to gear backlash.  For more information on backlash, click this article.

Here is a visual from Celestron's Product Manager for Astronomy, Lance Lucero.