When a phalaenopsis orchid plant finishes blooming, trim the flower stem just underneath the first bloom and above the first leaf node. It is possible for a new flower stem to branch out from the leaf node. A lot of patience is required though, as it takes a few weeks, while the plant works hard to produce more flowers. Put your plant in a room with an east or northeast exposure and ignore it.
Using a weak solution of an orchid fertilizer will keep your plant healthy and encourages the plant to flower again. I recommend using Schultz Orchid Plant Food or a flowering plant food, 15-30-15, at a quarter strength. The potting material contains minimal nutrition, so it is necessary to fertilize weakly and frequently. Every watering is best. Store the unused portion of fertilizer solution in a jar or bottle in your cupboard. Just take it out to use at the next watering.