According to the American Orchid Society, orchids are propagated or grown through division, back bulbs, offshoots and seeds. Because seed propagation can be difficult and result in hybrid plants, it is not the recommended method for beginning gardeners.
Orchids can be propagated through division, which requires a mature plant. The orchid first needs to be removed from its container. It can then be divided or cut into pieces as long as each piece has a lead or new growth. The divided orchid needs to be planted in new containers, but not watered until the roots start to grow.
An orchid that has only one lead can still be divided, but the other pieces may contain back bulbs. Back bulbs are growths with dormant eyes that can start growing if activated. These bulbs need to be planted in a small pot filled with sphagnum moss with the eyes above the surface of the moss. They should then be kept humid and sprayed with water daily until they start growing.
An orchid can also be grown by cutting an offshoot from a parent plant. It can then be planted in sphagnum moss. In order to grow, it needs to be kept in a warm, humid environment.