Make sure the spike has dried before you do it. Paphs and Cattleyas are propagated by cutting the rhizome into sections that contain at least 4 starts and replanting the sections in new, smaller pots. The Phals grow from only one crown, so cannot be divided. These can be cut off and potted up. They will all need to be staked until the roots have formed a new anchorage for the plant.
Light is the most limiting factor in orchid culture.
If they do not get enough light, they won't bloom, no matter what else you do. If you think the light is strong enough, the problem may be that it is not long enough each day. Another problem might be that the plant has been recently repotted or moved to a new location. Over-watering will usually turn the buds black before they fall off. I've done everything right and the orchid did not rebloom this year.