Making a Dobsonian mount is beyond the scope of this article, but there are plenty of web resources that cover the issue. If you have a shaky equatorial drive, check the gears to see if there is any chance of adjusting them. The idea is to have a good tight contact between the ring gear, and the worm gear. If there is no adjustment, your best inexpensive solution is to apply some more of that heavy grease. This won't completely cure bad backlash, but it will help damp out vibrations.
Nothing beats weight in a tripod.
As likely as not, the tripod that comes with the scope is a very light affair, and mounting the telescope on it gives it a high center of gravity. This is not good. Fear not, Weedhopper, you will not have to carry the weight of the world on your shoulders. The answer to this mystery of life is to place a hook on the center post or center of the tripod, make a cloth bag to hang from that hook that can hold local rocks that you pick up at the observing sight. You can also use bottles of water, your significant other, whatever is handy.