The easiest way I know to do this is to digitize a path around the object in question in ArcScene (make sure your polyline contains z-values), then select this path and use the animations toolbar to create a flyby from path. When you do this, you should have your screen centered on the object you want to focus on. Right click on the object and select "Set Target and Center." Under path destination, select "Move observer along path with current target"
This will focus the camera on wherever you have the map centered as the animation flies along the path. For best results, I recommend a vertical offset from the ground elevation of your path. Use the animation controls options to preview the animation and change its duration.
When you are satisfied, use the animations pull down menu to export the animation as an AVI.
You should also check out this tutorial.