Do you see black borders around your video displaying in the monitor while it is still in the Edit Mode of Premiere Elements 10?
Have you selected the correct project preset? First thing that you need to determine are the properties of your source media. If you do not know this information from your camera and its settings, then you can use a free properties read out program such as MediaInfo.
You want to know video compression, audio compression, frame size, frame rate, file extension, aspect ratio, scan type (progressive or interlaced), scan order (if interlaced, upper or lower field first). That information should direct your choice of the project preset in the new project dialog. You want a project preset that matches the properties of your source video. Often if you have selected the wrong project preset, the program will let you know when you drag the file to the Timeline for the first time in that project.
A match will insure (among other things) that the program will set up the correct space in the Edit Mode Monitor for editing purposes. The other half of the equation is the export settings. How do you intend to export your Timeline content? Once we know source media properties and project preset details then we can focus in on the details of the export choice and it specific settings.
If you supply that initial information, all will be able to suggest ways to avoid some issues that you are running into.
Thanks. We will be watching for your follow up.
As others have stated, black bars, whether on all sides, letterboxed (top and bottom), or pillarboxed (both sides), are a result of a mis-match between the Sequence/Project settings, and the Source material, or if on output, between the Sequence/Project and the Export/Share settings. This article addresses those mis-matches: http://forums.adobe.com/message/3797172#3797172