Answer: Once the foliage is completely dry and brown it should come away with a gentle tug. That's when you can dig the bulbs (or take them out of the pot) and shake off the dirt. Allow them to air dry in the sun for a day or so (protect from dew) and when quite dry, store. They do best in a dark, room temperature place but most important, a dry place. You can put them in a single layer on a shelf in say a garage, or in a paper bag to keep them dark. Do not store them in a plastic bag.
In the fall as soon as the soil temperature drops you can plant them in the ground. If you have to grow them as container plants, then you will need to chill them. Here are directions on how to force tulip bulbs indoors. You may need to cut and paste the complete url into your browser to make it work correctly.
There are two cautions here. One is that many of the varieties sold as container/florist plants may not perform well under garden conditions. The other is that usually the container grown plants just fail to thrive the next year. The artifical forcing process is very stressful and too often the foliage is not able to provide the bulb with enough energy to allow it to bloom the next year. So while you can try this and see if it works, you should probably consider it an experiment and not be too disappointed if it doesn't. Have fun with your project!
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