This is aimed at Premiere Pro, but may help
A link with many ideas about computer setup http://forums.adobe.com/thread/436215?tstart=0
Work through all of the steps (ideas) listed at http://ppro.wikia.com/wiki/Troubleshooting
If your problem isn't fixed after you follow all of the steps, report back with ALL OF THE DETAILS asked for in the FINALLY section, the questions at the end of the troubleshooting link... most especially the codec used... see Question 1
Again... report back with ALL OF THE DETAILS asked for in the FINALLY section
Welcome to the forum.
I agree with John, on the details of your Export.
As this is possibly not a system issue (could be, but let's keep that for later), I'd concentrate on details of your Assets (your source Video), your Project Preset and on the settings that you are using for Export/Share*. This ARTICLE will give you some tips on both finding the details, if you do not have them handy, and also the types of info that will be very useful.
Also, please let us know about the playback where you are observing this shakiness, i.e. one a DVD-Video played on a computer, or on a set-top player hooked to a TV, or maybe as an AV file, in a software player. There can be different causes, depending on where and how one is viewing.
* The reason that these terms are listed together is that in earlier versions of PrE, the more general term was "Export," but in later versions, the operations were grouped under the Share tab, rather than being split. The operation is still exporting, but the location of this has now been grouped in one place, regardless of format/CODEC. It can be a bit confusing, and I try to cover all bases with "Export/Share."
And let us know what kind of camcorder this video came from.
The chief cause for shakiness in video is that your video source was not matched to the correct project preset.
I have had this problem also. I think it has something to do with the links between the project and the clips, the log file etc. Try this: Click on the source clip in your project window, then right click on the corresponding clip in the timeline and select "Replace with clip from project". Do this with the video clips in the timeline and then go to the Share area and select your output. This is much simpler than worrying about interlacing settings, and it has fixed the problem for me.