Hi Jini you could sow the tulip seeds but it will take three to five years for them to reach flowering size. Fill a pot, not a seed tray, with potting compost, moisten slightly, sprinkle on the seed, cover with grit, label (very important) and stick somewhere out of the way and forget about for a year. Check next spring to see if there is any 'grass' growing this will be the new tulips.
The seed will not necessarily produce the same tulip as the parent unless you only have one variety of tulip in your garden.

Most modern Tulips are complex hybrids, so even self-pollinated seedlings will show a variety of characteristics, as their parent's genes re-sort themselves.
The seedlings look like grass, as Moon_Grower says, but they will have pea-sized bulbs at the base, at the end of next spring's growing season--as long as you keep them lightly fed while they have leaves. Keep the bulbs in the pot over the rest of the summer, and keep them reasonably dry. In fall, plant them either in the ground, about three times as deep as they are wide, or at the same depth in their own pots. You might want to keep the runts, too--sometimes the slower growing plants produce bigger and/or brighter flowers than their big brothers. Each year the leaves get larger and more numerous, and the bulbs get bigger and need to be planted deeper, until you have your very own variety of Tulip!

Thanks Tugb. forgot to say to feed when the leaves are up, you'll need to do this every year Jini.