One of the major problems with cheap telescopes is the mounts tend to be wobbly and prone to vibration. Without buying an expensive mount you probably will not be able to eliminate all the vibration but you can reduce it a great deal.
Mounts for cheap scopes fall into 3 classes:
German Equatorial Mount (GEM)
Fork
Dobson
I've never had a dobson mount so I can't not speak of them from experience.
Small Forks and GEMs have one thing in common, they are both normally on top of a tripod. There are a number of things you can do with tripods to make them more stable. First, drop them as low as you can. The shorter the legs are the less vibration you will get from the tripod. This will require you to be seated when viewing, but this has an added bonus of being a more comfortable position enabling you to concentrate on your view.
The second thing to do with a small tripod is to make sure all the bolts and screws are tight. Not just finger tight, if they have wing nuts use a pair of plyers, if hex nuts a wrench, and snug them down. this will help more than some people think.
A third thing that sometimes will help if the tripod is still wobbly is to hang a weight (like a gallon jug of water) from the center of the tripod.
GEMs. If your mount is something like this, it is a German Equatorial Mount:
A scope on a GEM needs to be balanced almost but not quite. There is a counter weight on a shaft that can be moved up or down the shift. First, find the balance point. It is balanced when, with the clutch released, the scope will move either direction without trying to move back. After you find the balance point move the weight slightly from the balance point and lock it down. The reason you want it slightly out of balance is this: If it is exactly balanced and there is any slop in the gears (and there always is in a cheap GEM) it will oscillate every time you move the slow motion control. With it slightly out of balance there will be a slight amount of weight on the worm gear preventing the oscillation.
A GEM mount need to be lubricated occasionaly. While there are a number of schools of thought about it, prevailing wisdom says to use a high quality light weight lithium grease. With a high quality GEM I would agree, but not with cheap eq1 or eq2 GEMs that come with 60mm refractors or other cheap small scopes. These little mounts are built to loose specs, and have a certain amount of slop built into them. I use a "anti-corrosion" grease designed for outboard motors:
This is a very heavy, very sticky (almost like glue) grease that actually takes some of the slop out of one of these mounts. When I relube a mount, I take it apart and totally coat the shafts with grease, enough so that when I put it back together some of the grease is squeezed out. I put a light coat of grease on all the gears and work the mount through a complete rotation then wipe the excess that has built up on the worm gears off. I do this about every 3 months.
Fork Mounts. An example of a scope mounted on a fork mount:
I personally don't like the little fork mounts that come with some 60mm refractors because they tend to vibrate more than the cheap GEMS and have remounted one scope because of this. You can add a couple of rubber washers between the forks and the scope and tighten the two thumb bolts that go into each side of the scope down solid. It will help a little, but can make the scope a little harder to aim.
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