Traditionally...for whatever reason...if you're right handed you fish a spinning outfit with the rod in your right hand, and reel with your left hand. With a baitcaster, right handers typically hold the rod with their left hand, and reel with their right hand. However, some folks will use their right hand to cast, and then switch the rod to the other hand to reel with their right hand. Then to make it even more confusing, some will cast with their left hand, but switch to their right hand to "figure 8" at the end of the retrieve.
Bottom line...just fish the way that's most comfortable for you. Some guys like the rod in their dominant hand, and some prefer to reel with their dominant hand. I don't think there are any "rules".