It's a dieffenbachia. I like diefs.
Cut the canes back to about 6" above the soil surface. New branches will sprout from the sides of the stubs that are left.
Cut the leafy top off, leaving a piece of cane attached that, when planted in the soil, supports the top at an attractive height. (Perhaps a foot or 18"? Just use your own judgement to decide what you think looks nice.)
Finally, take the remaining pieces of the canes and cut them into sections. I like to leave 2 nodes per section. (The nodes are the little ridges that encircle the cane.) Make your cuts midway between 2 nodes. Set the sections aside for anywhere from 24 hours up to a few days ... even a week, if need be. What you want is for all the cut ends of the cane sections to dry and become hard. This is called "callousing over". Be sure to do this with the cut end of the leafy top section, too!
When the ends have calloused, plant the stems of the leafy top sections in a pot of fresh, moist-but-not-wet soil. Be careful not to overwater them, because there are no roots to absorb water from the soil. Roots will form quickly, though, and you will have nice new plants.
Lay the other cut sections of cane horizontally, on their sides, buried about halfway in a moist, sterile medium, such as clean sharp sand or plain perlite. Place them in bright, indirect light. Each section will sprout new stems and roots, and become a whole new plant. You'll have pretty gifts for all your friends! (And maybe even a few strangers!
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams