I have tulips that I planted in the fall of 2000 and they still bloom every
spring for me. I cut off the flower at the top of the stem after the bloom has
waned, and just let the leaves die off naturally.
Last fall I dug up the bulbs and split them (they grow new bulbs that remind me
of cloves of garlic) and the smaller bulbs will need another winter before they
produce a flower.
If your bulbs are in a pot, you can cut the flower off, let the leaves die off,
then in the fall plant them in a sunny spot, and plant them as deep as their
length (a one inch bulb should be at least one inch in the ground) and plant
them pointy end up!
If you want to keep them in the pot, you can, just keep the pot in a cool spot
in the winter.