How do I care for tulips, and what should I do after the petals have fallen off, leaving behind just the stem and leaves?

Once your tulips have finished blooming and the petals have fallen, remove the flower stem by cutting it at the base, or snap off the faded flowers being sure to take the base of the flower. Now allow the foliage to grow and mature and ripen. When it turns brown and comes off easily in your hand, collect the old foliage and dispose of it in the trash. The bulbs should emerge again next spring. You might give them some complete granular fertilizer in the fall when they begin to root and again in early spring when they begin to come through the soil.