How does one move over a center of gravity/mass?

Center of gravity is not the average location of an object. Center of gravity is a point where the object can be balanced, and will stay there until the application of an external source of energy.

For a general shaped object, there is a simple mechanical way to determine the center of gravity:

1) If we just balance the object using a string or an edge, the point at which the object is balanced is the center of gravity. (Just like balancing a pencil on your finger!)
2) Another, more complicated way, is a two step method shown on the slide. In Step 1, you hang the object from any point and you drop a weighted string from the same point. Draw a line on the object along the string. For Step 2, repeat the procedure from another point on the object You now have two lines drawn on the object which intersect. The center of gravity is the point where the lines intersect. This procedure works well for irregularly shaped objects that are hard to balance.

Make sure you review the source shown below.

By the way, is this for a specific homework question? If it is, post it word for word.