You don't necessarily have to move them. It depends on what kind of tulips you got. If you got Emperors, Darwins or Triumphs and especially species tulips, they could come back happily next year and bloom again so just leave them in place. If they're one of the fancy hybrids, chances are they wouldn't flower again (although you might get a second year), so you might just as well dig them up and throw them in the compost when they're finished blooming.

If you want to keep them, but absolutely want them out of the bed because you can't live with the leaves, you can use the rather labour-intensive method of heeling in, which involves carefully digging up the bulbs without damaging leaves or bulbs and settling them into a shallow trench in an out-of-the-way place (lining it with chicken wire will make it easier to lift them later), and letting them complete their life cycle there. Once the leaves have completely dried, dig up the bulbs, clean and dry them, and store them in a cool, dry place for planting in the fall.

If you decide to leave them in place, don't cut the leaves back until they've lost all of their green colour. The leaves are feeding the bulbs for next year's flowers.

Hope this helps some.

Janet's Garden Blog

Move them when the foliage is mostly dead. You can store them over the summer and replant in autumn.

My garden has had tulips come up every year for more than ten years and they are beautiful but they need to be moved. (better stated reorganized) Can I dig them up and replant them with out hurting them?