Ed, You can find all these answers in the archive if you just enter "draceana" and 180 days. Basically, cut it wherever you want, Cut the cut-off piece into as many bits as you want. Stick the base of each piece an inch or two into a free-draining mix and water carefully. Roots will form in about six weeks if you keep it in a warm place.
The nurseries do all their propagation this way, using cane which usually comes in from Central America with all the leaves stripped off. I would take the same path since most of the leaves that you leave on will die. The exception is the tip piece which will keep at least some of its leaves through the rooting. Your plant which splits into three must have flowered at that height - that is the typical aftermath of having the terminal bud convert into flowers. Derek