I have two bikes with this kind of adjustable stem for handlebar. It is using a simple "tooth" that hold it on position. If it is not tightened properly, the tooth will be grinded down and become lose after sometime(that cause the wobble).
To check it out, you need two wrench(with hex bits) or hex key. Wrench with hex bit is recommended, because it gave you enough torque to twist open the screw. One side turning at opposite direction while another holding the screw from turning.
After you loosen the joined screw, you will know what I mean. Now adjust the handlebar and make it "locked" properly, then tighten the screw. Make sure you make it very tight (I don't have an expensive torque wrench to measure the torque) when you place the screw back.
The funny part of these kind of adjustable stem, is the "lawyer notes sticker" mentioned in Sheldon brown hands up article. Both of my bike come with this sticker. I have better quality adjustable stem on my touring bike, which you don't need much force to tighten the screw and only one hex key is required to adjust the stem.
(Photo borrow from Sheldon Brown website, http://www.sheldonbrown.com/handsup.html )