After flowering, clip the dead flower off the stem, and let the foliage die off while maintaining water level. When the foliage has completed drying out, you may see new little bulbs beginning to form, leave these.
Cut the foliage, but leave the roots, and store the bulbs dry and as cool as possible until early November. Then plant them in your garden, using a good mix of soil and compost. Thoroughly water them at planting.
When and where to plant (in my zone) after flowering?
Zones 4 & 5 - September or early October
Zones 6 & 7 - October to early November
Zones 8 & 9 - November to early December
Zone 10 - Late December to early January
Refrigerate tulips bulbs for six to eight weeks before planting in zones 8 through 10, place them in a paper bag away from ripening fruits (the fruits produce ethylene gas, which destroys the flower bud within the bulb).
Tulips grow best in full sun in well-prepared soil with fast drainage. Avoid planting where water collects, or in locations that are prone to late frosts.
You can find your planting zone here: USDA Plant Hardiness Zone Map
If you'd like to attempt to make them grow on water again, have a look here: Can the bulbs grow on water again?