Your plant is a Dieffenbachia, you can cut the top off and reroot it in either water or sterile potting mix. The bare stalk on the mother plant will send out a new shoot or two. It's normal to lose the bottom leaves.

Dieffenbachia

care

When you cut the stem, a white latex type sap will get all over the place.

It's growing towards your florescent lighting by the way. It's care is exactly what the others have said. It is in fact a relative of the 'lucky bamboo' plants which are not bamboo by the way. You can cut them low to the pot so that new growths will florish from below and bush out making the plant more lush. Then with the cut off stem, you can cut them out into smaller pieces and root them in water first and in pots later. Remove the bottom leaves where the trunk needs to be set in the ground. Easy. The large kinds of this plant with thick trunks can be set in water for even years.

Ianna