The best example I’ve seen of how the right & left brain hemispheres work, comes from Betty Edwards book, “Drawing From The Right Side Of The Brain”.
In her book there is a drawing exercise, where you can actually feel a "pull" from the left “dominance & control” side of the brain, to abandon the exercise. But if you stay with it, once the left brain relinquishes it’s control, the right side carries on with what does best...and real drawing begins.

Edwards explains that RIGHT brain thinkers tend to ignore the...“this is a waste of time” message sent out by the left brain and are able to go directly into the right-brain-creative drawing mode. Her point is that left brain thinkers CAN also be taught to ignore the “control” messages and learn to “see” and...learn to draw. Many left brain thinkers have to re-learn to use their right brain before they can learn to draw again. (We all knew how to draw as children, our "crayon-scribbles-on-the-wall" were simply acts of self expression.)

We still have to avoid the tendency of the left brain to “compare and analyze” our drawing. It doesn’t matter how good your drawing is compared to mine,.. it’s about the benefit to your “whole being” from having a right brain experience. Right brain experiences tend to linger and help us feel more complete and “in the now”, as well as leave us feeling passionate about our lives. Passionate people tend to set the bench mark for what happiness is!