Usually i do it by making a curve circle then parent (ctrl+p) the camera to follow the path. Of course make it so the object you wish to rotate around is in the centre of the circle. Also make sure the circle is scaled correctly or move the camera so it is far enough away from the object. Then add the track to constraint to the camera (F7) then put the name of the object which is most central into the constraint (found at the bottom left of the 3d window in grey). You may have to adjust the angle etc. of the camera or use the x,y and z options within the contraint window to re-adjust it.Then once its set up for rendering i would move the curve circle to a different layer (M) that is not set for rendering (F10 > left hand side >render layers), only move the curve circle not the camera.
This is how i used to do it if i remember correctly.
Hope it Helps
Sorry if you know all the commands i just put them in incase someone else who doesn’t know them reads this for the same purpose.