A basal keiki forms at the base of the plant near the lowest leaf. This type of baby plant can be left on the mother plant indefinitely. It will send its own root system into the mix and start feeding itself fairly quickly, so it is not a drain on the mother plant. It will send up its own flower spike and bloom.
Keikis can appear on the flower stem. First a set of leaves will form, then roots. It is best to leave the keiki on the mother plant until the keiki blooms, at which time it will have developed enough strength and roots to be weaned from the mother plant. Gently twist the keiki off the mother plant after its blooms fall and pot it in a 3- to 4-inch pot of its own. Remember to fertilize the mother plant. She is eating for two.
Sometimes an orchid plant in severe distress will try to either throw a keiki or produce a bloom spike. This is a last-gasp effort to perpetrate the species. Unfortunately, the plant does not have the energy to complete the effort and it will deplete the plant to the point of death. If your mother plant has lost a lot of leaves, has wrinkled leaves, or is in stress for some other reason, do not let it produce keikis or blossoms. Snap them off to save the mother plant.