Lucky bamboo plants are members of the dracaena family. They're not actually bamboo--they're houseplants. Easy to care for and easy to propagate, your bamboo plants will provide you with many fresh stems if you root healthy cuttings properly. Aside from a weekly change of water to help keep them healthy, your lucky bamboo plant and its cuttings don't need much care.
Take a cutting from your own or a friend's plant. Just use a sharp knife and cut directly across the parent stem 1/4-inch above a joint to produce the new "baby" stem.
Place the lucky bamboo stem you want to root in a glass of non-fluoridated, non-chlorinated water. If your tap water has fluoride and chlorine in it, try using bottled spring water.
Check the water level in the glass every day and replenish as necessary to maintain a consistent water level around the bamboo stem. Ideally the water should cover the bottom 2 to 3 inches of the stem to encourage rooting.
Move the freshly rooted lucky bamboo stem to a permanent home once it has roots that are 2 or 3 inches long. You might place it back in the arrangement next to the stem it was cut from, or start an entirely new arrangement. If you start a new arrangement, make sure to include enough gravel--try aquarium gravel--to hold the stem steady and keep it from tipping over.